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An odd thought...

JustCallMeTarzan
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3/7/2011 12:42:53 PM
Posted: 5 years ago
Supposing we accept for the moment that the universe does in fact have a speed limit of the speed of light (C). Let's also assume that the law of inertia imparts a perfect constant in space - i.e. if something in space is traveling .8C, when thrust stops, it will continue to travel .8C until something stops it.

Ok... so say we have a device that moves a boom in an arc. The base of the boom moves at a speed of .5C (and I realize this is better expressed in degrees or radians per second, but it doesn't matter). And this boom is also long enough that while the end of the boom moves at the same degrees/time speed, the actual distance/time speed is really 2.0C.

There's a spaceship attached to the end of the boom that is released at the end of the swing.

Wouldn't the spaceship move at 2.0C?
Ore_Ele
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3/7/2011 1:04:46 PM
Posted: 5 years ago
At 3/7/2011 12:42:53 PM, JustCallMeTarzan wrote:
Supposing we accept for the moment that the universe does in fact have a speed limit of the speed of light (C). Let's also assume that the law of inertia imparts a perfect constant in space - i.e. if something in space is traveling .8C, when thrust stops, it will continue to travel .8C until something stops it.

Ok... so say we have a device that moves a boom in an arc. The base of the boom moves at a speed of .5C (and I realize this is better expressed in degrees or radians per second, but it doesn't matter). And this boom is also long enough that while the end of the boom moves at the same degrees/time speed, the actual distance/time speed is really 2.0C.

There's a spaceship attached to the end of the boom that is released at the end of the swing.

Wouldn't the spaceship move at 2.0C?

No. The boom could not be accelerated so that the end of it was moving at such a speed.

As the end accelerates and approaches 1C (the speed of light), its inertia would increase, causing acceleration of the entire boom to minimize.
"Wanting Red Rhino Pill to have gender"
Ore_Ele
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3/7/2011 1:05:31 PM
Posted: 5 years ago
At 3/7/2011 1:02:59 PM, Greyparrot wrote:
I thought there is no real speed limit since time is not relatively constant?

time with respect to a given frame.
"Wanting Red Rhino Pill to have gender"
Ore_Ele
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3/7/2011 1:09:24 PM
Posted: 5 years ago
At 3/7/2011 12:42:53 PM, JustCallMeTarzan wrote:
Supposing we accept for the moment that the universe does in fact have a speed limit of the speed of light (C). Let's also assume that the law of inertia imparts a perfect constant in space - i.e. if something in space is traveling .8C, when thrust stops, it will continue to travel .8C until something stops it.

Ok... so say we have a device that moves a boom in an arc. The base of the boom moves at a speed of .5C (and I realize this is better expressed in degrees or radians per second, but it doesn't matter). And this boom is also long enough that while the end of the boom moves at the same degrees/time speed, the actual distance/time speed is really 2.0C.

There's a spaceship attached to the end of the boom that is released at the end of the swing.

Wouldn't the spaceship move at 2.0C?

I just thought of an extention of this, which might be of interest.

Let's say we have the spinning boom, and the end of it is spinning at .99C (since we could not accelerate it faster than that). At the end, we have a spaceship tied to a teather which would extend to a length of twice the boom. If the ship is released, it will go out until the teather grabs ahold of it and swings it into an orbit like path (like how a space elevator would work). This should extend past where it would be 1C (to about 1.98C), what would happen in that case.

I'll have to look into it.
"Wanting Red Rhino Pill to have gender"
JustCallMeTarzan
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3/7/2011 4:47:55 PM
Posted: 5 years ago
At 3/7/2011 1:09:24 PM, OreEle wrote:

I just thought of an extention of this, which might be of interest.

Let's say we have the spinning boom, and the end of it is spinning at .99C (since we could not accelerate it faster than that). At the end, we have a spaceship tied to a teather which would extend to a length of twice the boom. If the ship is released, it will go out until the teather grabs ahold of it and swings it into an orbit like path (like how a space elevator would work). This should extend past where it would be 1C (to about 1.98C), what would happen in that case.

I'll have to look into it.

But isn't that the same principle? We don't have to accelerate the end of the boom past 1C - we just have to accelerate the close end of the boom to whatever speed is necessary to get the end to move at 1C.

So assume the boom is about 100 miles long - so the path of a full circle is, very roughly, 600 miles. To launch a spaceship off the boom at 1C, it has to make a full revolution in about 3 thousandths of a second (~0.003226). That makes it at 333 revolutions per second, or just shy of 20K RPM.

The tech exists now to make 20,000 RPM motors, but there is of course the problem of torque - a problem I leave to future generations to solve =P
Ore_Ele
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3/7/2011 4:55:52 PM
Posted: 5 years ago
At 3/7/2011 4:47:55 PM, JustCallMeTarzan wrote:
At 3/7/2011 1:09:24 PM, OreEle wrote:

I just thought of an extention of this, which might be of interest.

Let's say we have the spinning boom, and the end of it is spinning at .99C (since we could not accelerate it faster than that). At the end, we have a spaceship tied to a teather which would extend to a length of twice the boom. If the ship is released, it will go out until the teather grabs ahold of it and swings it into an orbit like path (like how a space elevator would work). This should extend past where it would be 1C (to about 1.98C), what would happen in that case.

I'll have to look into it.

But isn't that the same principle? We don't have to accelerate the end of the boom past 1C - we just have to accelerate the close end of the boom to whatever speed is necessary to get the end to move at 1C.

So assume the boom is about 100 miles long - so the path of a full circle is, very roughly, 600 miles. To launch a spaceship off the boom at 1C, it has to make a full revolution in about 3 thousandths of a second (~0.003226). That makes it at 333 revolutions per second, or just shy of 20K RPM.

The tech exists now to make 20,000 RPM motors, but there is of course the problem of torque - a problem I leave to future generations to solve =P

Yes, but the torque is a function of the mass/inertia. As the end of the boom accelerates towards 1C, the inertia grows, thus causeing future acceleration to be minimized to the limit where it will not pass 1C velocity.

But in the case where it is on a teather, you can get it spinning at the correct rotational velocity, then release the object on the teather, and it should be moving faster than light.
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belle
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3/7/2011 4:57:52 PM
Posted: 5 years ago
At 3/7/2011 1:09:24 PM, OreEle wrote:
At 3/7/2011 12:42:53 PM, JustCallMeTarzan wrote:
Supposing we accept for the moment that the universe does in fact have a speed limit of the speed of light (C). Let's also assume that the law of inertia imparts a perfect constant in space - i.e. if something in space is traveling .8C, when thrust stops, it will continue to travel .8C until something stops it.

Ok... so say we have a device that moves a boom in an arc. The base of the boom moves at a speed of .5C (and I realize this is better expressed in degrees or radians per second, but it doesn't matter). And this boom is also long enough that while the end of the boom moves at the same degrees/time speed, the actual distance/time speed is really 2.0C.

There's a spaceship attached to the end of the boom that is released at the end of the swing.

Wouldn't the spaceship move at 2.0C?

I just thought of an extention of this, which might be of interest.

Let's say we have the spinning boom, and the end of it is spinning at .99C (since we could not accelerate it faster than that). At the end, we have a spaceship tied to a teather which would extend to a length of twice the boom. If the ship is released, it will go out until the teather grabs ahold of it and swings it into an orbit like path (like how a space elevator would work). This should extend past where it would be 1C (to about 1.98C), what would happen in that case.

I'll have to look into it.

should still have the same problem though. as the spaceship extends outwards it still can't go any faster than the speed of light, so it just slows the whole contraption down.
evidently i only come to ddo to avoid doing homework...
Ore_Ele
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3/7/2011 5:26:50 PM
Posted: 5 years ago
At 3/7/2011 4:57:52 PM, belle wrote:
At 3/7/2011 1:09:24 PM, OreEle wrote:
At 3/7/2011 12:42:53 PM, JustCallMeTarzan wrote:
Supposing we accept for the moment that the universe does in fact have a speed limit of the speed of light (C). Let's also assume that the law of inertia imparts a perfect constant in space - i.e. if something in space is traveling .8C, when thrust stops, it will continue to travel .8C until something stops it.

Ok... so say we have a device that moves a boom in an arc. The base of the boom moves at a speed of .5C (and I realize this is better expressed in degrees or radians per second, but it doesn't matter). And this boom is also long enough that while the end of the boom moves at the same degrees/time speed, the actual distance/time speed is really 2.0C.

There's a spaceship attached to the end of the boom that is released at the end of the swing.

Wouldn't the spaceship move at 2.0C?

I just thought of an extention of this, which might be of interest.

Let's say we have the spinning boom, and the end of it is spinning at .99C (since we could not accelerate it faster than that). At the end, we have a spaceship tied to a teather which would extend to a length of twice the boom. If the ship is released, it will go out until the teather grabs ahold of it and swings it into an orbit like path (like how a space elevator would work). This should extend past where it would be 1C (to about 1.98C), what would happen in that case.

I'll have to look into it.

should still have the same problem though. as the spaceship extends outwards it still can't go any faster than the speed of light, so it just slows the whole contraption down.

But imagine the distructive forces involved in that. Since the boom is near the speed of light at the tips, it is going to have a massive mass (lol), and since the spaceship, when first released, is going to be going at near the speed of light, it is going to be reaching the point where it should be going over the speed of light in fraction of a milisecond, and to balance, the boom is going to have to slow down by 1/2 of its rotational velocity (we used an example where the teather was the length of the boom) in that short time.
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belle
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3/7/2011 5:33:42 PM
Posted: 5 years ago
At 3/7/2011 5:26:50 PM, OreEle wrote:
At 3/7/2011 4:57:52 PM, belle wrote:
At 3/7/2011 1:09:24 PM, OreEle wrote:
At 3/7/2011 12:42:53 PM, JustCallMeTarzan wrote:
Supposing we accept for the moment that the universe does in fact have a speed limit of the speed of light (C). Let's also assume that the law of inertia imparts a perfect constant in space - i.e. if something in space is traveling .8C, when thrust stops, it will continue to travel .8C until something stops it.

Ok... so say we have a device that moves a boom in an arc. The base of the boom moves at a speed of .5C (and I realize this is better expressed in degrees or radians per second, but it doesn't matter). And this boom is also long enough that while the end of the boom moves at the same degrees/time speed, the actual distance/time speed is really 2.0C.

There's a spaceship attached to the end of the boom that is released at the end of the swing.

Wouldn't the spaceship move at 2.0C?

I just thought of an extention of this, which might be of interest.

Let's say we have the spinning boom, and the end of it is spinning at .99C (since we could not accelerate it faster than that). At the end, we have a spaceship tied to a teather which would extend to a length of twice the boom. If the ship is released, it will go out until the teather grabs ahold of it and swings it into an orbit like path (like how a space elevator would work). This should extend past where it would be 1C (to about 1.98C), what would happen in that case.

I'll have to look into it.

should still have the same problem though. as the spaceship extends outwards it still can't go any faster than the speed of light, so it just slows the whole contraption down.

But imagine the distructive forces involved in that. Since the boom is near the speed of light at the tips, it is going to have a massive mass (lol), and since the spaceship, when first released, is going to be going at near the speed of light, it is going to be reaching the point where it should be going over the speed of light in fraction of a milisecond, and to balance, the boom is going to have to slow down by 1/2 of its rotational velocity (we used an example where the teather was the length of the boom) in that short time.

so the boom snaps? lol... its not as though the tether will go straight out either, it will likely begin to trail behind rather quickly as the ship moves away from the end of the boom... so it would just be trailing until it ran out of tether, and then it would exert a massive force opposite to the direction of rotational motion... (assuming this is a flexible tether of course). and its not like it needs time to adjust in order to follow the laws of physics :P
evidently i only come to ddo to avoid doing homework...
Ore_Ele
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3/7/2011 5:41:22 PM
Posted: 5 years ago
At 3/7/2011 5:33:42 PM, belle wrote:
At 3/7/2011 5:26:50 PM, OreEle wrote:
At 3/7/2011 4:57:52 PM, belle wrote:
At 3/7/2011 1:09:24 PM, OreEle wrote:
At 3/7/2011 12:42:53 PM, JustCallMeTarzan wrote:
Supposing we accept for the moment that the universe does in fact have a speed limit of the speed of light (C). Let's also assume that the law of inertia imparts a perfect constant in space - i.e. if something in space is traveling .8C, when thrust stops, it will continue to travel .8C until something stops it.

Ok... so say we have a device that moves a boom in an arc. The base of the boom moves at a speed of .5C (and I realize this is better expressed in degrees or radians per second, but it doesn't matter). And this boom is also long enough that while the end of the boom moves at the same degrees/time speed, the actual distance/time speed is really 2.0C.

There's a spaceship attached to the end of the boom that is released at the end of the swing.

Wouldn't the spaceship move at 2.0C?

I just thought of an extention of this, which might be of interest.

Let's say we have the spinning boom, and the end of it is spinning at .99C (since we could not accelerate it faster than that). At the end, we have a spaceship tied to a teather which would extend to a length of twice the boom. If the ship is released, it will go out until the teather grabs ahold of it and swings it into an orbit like path (like how a space elevator would work). This should extend past where it would be 1C (to about 1.98C), what would happen in that case.

I'll have to look into it.

should still have the same problem though. as the spaceship extends outwards it still can't go any faster than the speed of light, so it just slows the whole contraption down.

But imagine the distructive forces involved in that. Since the boom is near the speed of light at the tips, it is going to have a massive mass (lol), and since the spaceship, when first released, is going to be going at near the speed of light, it is going to be reaching the point where it should be going over the speed of light in fraction of a milisecond, and to balance, the boom is going to have to slow down by 1/2 of its rotational velocity (we used an example where the teather was the length of the boom) in that short time.

so the boom snaps? lol... its not as though the tether will go straight out either, it will likely begin to trail behind rather quickly as the ship moves away from the end of the boom... so it would just be trailing until it ran out of tether, and then it would exert a massive force opposite to the direction of rotational motion... (assuming this is a flexible tether of course). and its not like it needs time to adjust in order to follow the laws of physics :P

Just like with a ball on a string, the faster you spin in, the more it straiten's out in a circle, it does not trail behind.
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belle
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3/7/2011 6:08:15 PM
Posted: 5 years ago
At 3/7/2011 5:41:22 PM, OreEle wrote:
Just like with a ball on a string, the faster you spin in, the more it straiten's out in a circle, it does not trail behind.

yes, thats because you're able to add enough force to accelerate the ball at the end. obviously in this case you would not be able to.
evidently i only come to ddo to avoid doing homework...
belle
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3/7/2011 6:14:27 PM
Posted: 5 years ago
At 3/7/2011 6:08:15 PM, belle wrote:
At 3/7/2011 5:41:22 PM, OreEle wrote:
Just like with a ball on a string, the faster you spin in, the more it straiten's out in a circle, it does not trail behind.

yes, thats because you're able to add enough force to accelerate the ball at the end. obviously in this case you would not be able to.

similarly if you don't supply enough force to the ball on the string it just falls down because gravity overcomes the small force you provide. if you did it in space though, the ball would lag behind!
evidently i only come to ddo to avoid doing homework...
Ore_Ele
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3/7/2011 6:15:01 PM
Posted: 5 years ago
At 3/7/2011 6:08:15 PM, belle wrote:
At 3/7/2011 5:41:22 PM, OreEle wrote:
Just like with a ball on a string, the faster you spin in, the more it straiten's out in a circle, it does not trail behind.

yes, thats because you're able to add enough force to accelerate the ball at the end. obviously in this case you would not be able to.

It's the centrifugal force (I know that is a pseudo force) that drives it straight out. And based on velocity vectors and force vectors, even at high speeds, it should be driven outwards, not trailing behind.

I suppose that the teather is just guarenteed to break, since in the nano seconds that the object hits tention with the teather, and it is attempting to accelerate from .99C to 1.98C, its inertia is going to jump towards infinite while in that split second of .99C to 1C, and the tension forces on the teather would then go to infinity and so ensure that the teather breaks.
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Ore_Ele
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3/7/2011 6:16:05 PM
Posted: 5 years ago
At 3/7/2011 6:14:27 PM, belle wrote:
At 3/7/2011 6:08:15 PM, belle wrote:
At 3/7/2011 5:41:22 PM, OreEle wrote:
Just like with a ball on a string, the faster you spin in, the more it straiten's out in a circle, it does not trail behind.

yes, thats because you're able to add enough force to accelerate the ball at the end. obviously in this case you would not be able to.

similarly if you don't supply enough force to the ball on the string it just falls down because gravity overcomes the small force you provide. if you did it in space though, the ball would lag behind!

it would only lag behind for a short while, until it reached the outside.
"Wanting Red Rhino Pill to have gender"
JustCallMeTarzan
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3/7/2011 6:16:54 PM
Posted: 5 years ago
Ok - I think I get it now - as the boom approached C, the amount of torque required to move the boom would approach oo ??

Wouldn't that do the same thing to a tether though? I would think for all intents and purposes a tether is just a less mechanically efficient boom...

What about compounded acceleration?? I.e. - I'm standing on the front of a ship that is moving .999C and I shoot my gun that has a muzzle velocity of .15C. How fast does the bullet go?
Ore_Ele
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3/7/2011 6:21:50 PM
Posted: 5 years ago
At 3/7/2011 6:16:54 PM, JustCallMeTarzan wrote:
Ok - I think I get it now - as the boom approached C, the amount of torque required to move the boom would approach oo ??

Wouldn't that do the same thing to a tether though? I would think for all intents and purposes a tether is just a less mechanically efficient boom...

well, it is a flexible boom (I'm thinking of a boom like a solid metal arm, so maybe we are thinking it differently).


What about compounded acceleration?? I.e. - I'm standing on the front of a ship that is moving .999C and I shoot my gun that has a muzzle velocity of .15C. How fast does the bullet go?

To an independent observer, the one that is standing still to observe you going .999c, the bullet would appear to be going .99915c

You would also, from your perspective, see light passing you, not at .001c, but at 1c still.
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belle
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3/7/2011 6:49:12 PM
Posted: 5 years ago
At 3/7/2011 6:16:05 PM, OreEle wrote:
At 3/7/2011 6:14:27 PM, belle wrote:
At 3/7/2011 6:08:15 PM, belle wrote:
At 3/7/2011 5:41:22 PM, OreEle wrote:
Just like with a ball on a string, the faster you spin in, the more it straiten's out in a circle, it does not trail behind.

yes, thats because you're able to add enough force to accelerate the ball at the end. obviously in this case you would not be able to.

similarly if you don't supply enough force to the ball on the string it just falls down because gravity overcomes the small force you provide. if you did it in space though, the ball would lag behind!

it would only lag behind for a short while, until it reached the outside.

i want to do that experiment. now that i think about it all the examples of "lagging behind" i can think of are caused by air resistance not a lack of force. i guess if you didn't apply enough force the system just wouldn't move.
evidently i only come to ddo to avoid doing homework...
mattrodstrom
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3/7/2011 6:58:29 PM
Posted: 5 years ago
At 3/7/2011 6:16:54 PM, JustCallMeTarzan wrote:
What about compounded acceleration?? I.e. - I'm standing on the front of a ship that is moving .999C and I shoot my gun that has a muzzle velocity of .15C. How fast does the bullet go?

Relative to what?

From my meagre understanding... that's the real question ;)

I would think it goes .15c relative to the ship... and .999C (plus just a lil bit) relative to the stuff the ship was moving that speed to... :/
"He who does not know how to put his will into things at least puts a meaning into them: that is, he believes there is a will in them already."

Metaphysics:
"The science.. which deals with the fundamental errors of mankind - but as if they were the fundamental truths."
mattrodstrom
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3/7/2011 7:05:02 PM
Posted: 5 years ago
and... though that Little bit that added to .999C isn't the .15C that was seemingly added... There's no reason to worry...

it doesn't have to make sense ;)
"He who does not know how to put his will into things at least puts a meaning into them: that is, he believes there is a will in them already."

Metaphysics:
"The science.. which deals with the fundamental errors of mankind - but as if they were the fundamental truths."
mattrodstrom
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3/7/2011 7:22:56 PM
Posted: 5 years ago
At 3/7/2011 6:58:29 PM, mattrodstrom wrote:
At 3/7/2011 6:16:54 PM, JustCallMeTarzan wrote:
What about compounded acceleration?? I.e. - I'm standing on the front of a ship that is moving .999C and I shoot my gun that has a muzzle velocity of .15C. How fast does the bullet go?

Relative to what?

From my meagre understanding... that's the real question ;)

I would think it goes .15c relative to the ship... and .999C (plus just a lil bit) relative to the stuff the ship was moving that speed to... :/

I'm thinking the reason for the discrepancy is that mass moving that speed distorts space itself... to the point where those things moving as such, From our standpoint, don't move as they would under regular (non-noticeable space distortion) conditions.

Meanwhile... In the system that is moving that fast away from us (lets say another galaxy) the projectile flies at .15C in a direction...

to us (who are separated from the event by such MASSIVE distortions in space) that additional (local) .15C is not nearly so much an addition...
"He who does not know how to put his will into things at least puts a meaning into them: that is, he believes there is a will in them already."

Metaphysics:
"The science.. which deals with the fundamental errors of mankind - but as if they were the fundamental truths."
JustCallMeTarzan
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3/8/2011 10:34:26 AM
Posted: 5 years ago
But if the bullet travels at .15C relative to the ship that is traveling at .999C relative to the observer, what is the actual speed of the bullet? It doesn't seem logical that it would be .99915C...

I guess a better question is what is the speed of the observer relative to the bullet? I would think it would be ("negative") 1.149C...
mattrodstrom
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3/8/2011 10:44:12 AM
Posted: 5 years ago
At 3/8/2011 10:34:26 AM, JustCallMeTarzan wrote:
But if the bullet travels at .15C relative to the ship that is traveling at .999C relative to the observer, what is the actual speed of the bullet? It doesn't seem logical that it would be .99915C...

nobody said things had to make sense.

I guess a better question is what is the speed of the observer relative to the bullet? I would think it would be ("negative") 1.149C...

nope.

more around ("negative") .999C

when "distance" is different... speed is different.

moving distorts space/distance.. moving Fast distorts it more... Moving at .999C distorts it INSANELY..

so... the fact that that added .15C becomes almost nothing at all, from a given perspective, really ought to be somewhat acceptable if you accept that the two areas of "space" (the distances) being compared differ massively.
"He who does not know how to put his will into things at least puts a meaning into them: that is, he believes there is a will in them already."

Metaphysics:
"The science.. which deals with the fundamental errors of mankind - but as if they were the fundamental truths."
Ore_Ele
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3/8/2011 11:15:20 AM
Posted: 5 years ago
At 3/8/2011 10:34:26 AM, JustCallMeTarzan wrote:
But if the bullet travels at .15C relative to the ship that is traveling at .999C relative to the observer, what is the actual speed of the bullet? It doesn't seem logical that it would be .99915C...

I guess a better question is what is the speed of the observer relative to the bullet? I would think it would be ("negative") 1.149C...

It's an issue with special relativity. We don't really know why these things happen, but from experiments in orbit and observations of the orbit of Mercury, we see that they are more accurate than standard newtonian physics.

For example, with the time effects of high speed travel, if standard newtonian physics were used on GPS satalites, they are only accurate to within several blocks of your location, but if special relativity is used, they can get within a few feet (because they go in orbit at speeds high enough for the effects to be marginally seen).
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Floid
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3/8/2011 12:32:24 PM
Posted: 5 years ago
At 3/8/2011 10:34:26 AM, JustCallMeTarzan wrote:
But if the bullet travels at .15C relative to the ship that is traveling at .999C relative to the observer, what is the actual speed of the bullet? It doesn't seem logical that it would be .99915C...

I guess a better question is what is the speed of the observer relative to the bullet? I would think it would be ("negative") 1.149C...

First you would calculate the velocity of the bullet relative to the observer using the formula from special relativity:

s = (v + u) / (1 + (v*u/c^2))

where v would be the velocity of the bullet and u the velocity of the ship.

The speed of the bullet relative the observer is 0.99926.

The speed of the observer relative to the bullet is the same thing, the velocity is the same but in the opposite direction (in relativity it doesn't matter who is moving and who is considered stationary).
Floid
Posts: 751
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3/8/2011 12:35:26 PM
Posted: 5 years ago
And notice from the above formula, since v and u always must be less then c, the formula can never result in a number greater than one... another affirmation that the speed of an object can never exceed the speed of light.
Ramshutu
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3/8/2011 4:36:46 PM
Posted: 5 years ago
At 3/8/2011 10:34:26 AM, JustCallMeTarzan wrote:
But if the bullet travels at .15C relative to the ship that is traveling at .999C relative to the observer, what is the actual speed of the bullet? It doesn't seem logical that it would be .99915C...

I guess a better question is what is the speed of the observer relative to the bullet? I would think it would be ("negative") 1.149C...

It maybe a good idea to consider what's actually going on here.

Lets say you are in a ship travelling at 0.99c and you shoot a gun at 0.15c. On the ship, the bullet would appear to travel at 0.15c away from you.

The trick to understanding why the speed of the bullet is not greater than the speed of light for an observer, is to consider how long the bullet takes to travel for the different observers.

Lets say that when you are in the ship, the bullet takes 1 second to cross the room you are in (yes, large room, I know!). Speed is a measure of distance/time; so you have the distance and the time, so therefore the speed.

However, because the ship is traveling close to the speed of light, the clocks you use to measure the bullet on the ship tick SLOWER than the observer watching the ship travel past.

This means if I was outside the ship and was measuring how long it took the bullet to cross the room, I would measure 30 seconds; because my clock is ticking faster.

This means to the observer, the bullet is travelling 1/30th of the speed.than the person on the ship; and to the observer, the bullet is still traveling slow than the speed of light, even with the speed of the ship.