Ed Wood
1. a observes an object b moving away from a @ .55C on a vector toward d which is not moving relative to a.
2. a sends a message to U to record the motion of object b relative to itself and d

a------>b V=.55C

a-------d V=0

3. d observes an object c moving away from d @ .55C on a vector toward a which as stated earlier is not moving relative to d.
4. d sends a message to U to record the relative motion of object c relative to itself and a.

d------->c V=.55C
d--------a V=0

4. To U the receiver of the information that these 2 objects are heading toward each other @ 1.1C

a------->b@.55C>?<c@.55C<-------d

What prevents this from happening?

Would U just say that even though the data he has received says these 2 objects are travel ling toward each other seemingly @ a velocity greater than C 1.1C that he should account for relativity and the 2 recordings are bad?

I think the premise is somewhat sound.

What am I missing?
waitedavid137
QUOTE (Ed Wood+Jul 16 2012, 01:52 PM)
4. To U the receiver of the information that these 2 objects are heading toward each other @ 1.1C

No, there is no real "toward eachother speed". To U object b is moving in the direction of object c at 0.55 and object c is moving in the direction of object b at 0.55 which overall situation you are confusing with the question of what is the velocity of object b according to object c or vica-versa.
Ed Wood
Given that there is no absolute reference frame. If there is no real speed between a and b how can there be any real speed limit?
waitedavid137
QUOTE (Ed Wood+Jul 17 2012, 06:32 AM)
Given that there is no absolute reference frame. If there is no real speed between a and b how can there be any real speed limit?

Because according to every observer, even one according to which one of the objects is at rest, every object moves at a speed that doesn't exceed c.
phyti
Ed doesn't give a location for U so we'll put him equidistant from a and d, or we can just ignore him.
The facts are there is a closing or relative speed in this case. This type of problem is solved everyday somewhere.
U's clock would record time of c-b encounter as distance (a-d)/.55c.
The technicality is, there is no object moving at 1.1c!
waitedavid137
QUOTE (phyti+Jul 17 2012, 07:59 AM)
Ed doesn't give a location for U so we'll put him equidistant from a and d, or we can just ignore him.
The facts are there is a closing or relative speed in this case. This type of problem is solved everyday somewhere.
U's clock would record time of c-b encounter as distance (a-d)/.55c.
The technicality is, there is no object moving at 1.1c!

I thought it understood that U was at rest with respect to a and d. There is no "actual closing speed". That "closing speed" which is valid is the speed of c with respect to b or vica versa which is not 1.1. Nothing travels at 1.1 so 1.1 is not the speed of anything. There just is no such actual closing speed.
phyti
QUOTE (waitedavid137+Jul 17 2012, 11:55 AM)
I thought it understood that U was at rest with respect to a and d. There is no "actual closing speed". That "closing speed" which is valid is the speed of c with respect to b or vica versa which is not 1.1. Nothing travels at 1.1 so 1.1 is not the speed of anything. There just is no such actual closing speed.

From the u reference the a-d gap is closed in (a-d)/1.1c (not .55, my error).
If a was 1.10 light seconds from d, the gap would have closed in 1 sec by the u clock. You're dealing with simultaneous motions. There is no violation of c because no object ever moved faster than c, and the limit applies to matter/mass.
If two cars moving 50 mph hit head-on, neither car goes 100 mph.
It's still about relative speed, rate of change of position. Light does not magically eliminate the concept.
waitedavid137
QUOTE (phyti+Jul 17 2012, 09:52 AM)

From the u reference the a-d gap is closed in (a-d)/1.1c (not .55, my error).
If a was 1.10 light seconds from d, the gap would have closed in 1 sec by the u clock. You're dealing with simultaneous motions. There is no violation of c because no object ever moved faster than c, and the limit applies to matter/mass.
If two cars moving 50 mph hit head-on, neither car goes 100 mph.
It's still about relative speed, rate of change of position. Light does not magically eliminate the concept.

Its not that the speed of light would eliminate the concept, its that the concept was wrong in the first place. Two 50mph cars closing at 100mph is the statement that one care moves at 100mph according to the other. This is relativistically wrong. One car moves at just under 100 mph according to the other. There is no actual 100mph closing speed of anything. According to any observer the actual speed of anything actual thing is less than or equal to c.
Maxila
QUOTE (waitedavid137+Jul 16 2012, 05:09 PM)
No, there is no real "toward eachother speed". To U object b is moving in the direction of object c at 0.55 and object c is moving in the direction of object b at 0.55 which overall situation you are confusing with the question of what is the velocity of object b according to object c or vica-versa.

David - I have a question about observed relative velocity of particles in an accelerator like CERN. For simplicity let's assume two particles are accelerated in opposite directions to .9c each, relative to the accelerator frame:

The instant before they collide, from each particles frame, what is the observed relative velocity between them?

Without giving it much thought, at first I'd assume it was 1.8c; however I realized from your answers to others in the thread that is the perspective from the accelerator frame. How do I calculate the observed relative velocity of the particles frame to each other?

I thought about it abstractly, and the answer seemed to be each particle frame would see the relative velocity between them as .9c, because of the observed length contraction in distance between each particle; is that correct?

Maxila
waitedavid137
QUOTE (Maxila+Jul 18 2012, 10:14 AM)
David - I have a question about observed relative velocity of particles in an accelerator like CERN. For simplicity let's assume two particles are accelerated in opposite directions to .9c each, relative to the accelerator frame:

The instant before they collide, from each particles frame, what is the observed relative velocity between them?

Without giving it much thought, at first I'd assume it was 1.8c; however I realized from your answers to others in the thread that is the perspective from the accelerator frame. How do I calculate the observed relative velocity of the particles frame to each other?

I thought about it abstractly, and the answer seemed to be each particle frame would see the relative velocity between them as .9c, because of the observed length contraction in distance between each particle; is that correct?

Maxila

The relativistic velocity composition for this case is equation 3.2.12 in section 2 of chapter 3 of Modern Relativity. The answer is about 0.994c.
Maxila
QUOTE (waitedavid137+Jul 18 2012, 10:43 PM)
The relativistic velocity composition for this case is equation 3.2.12 in section 2 of chapter 3 of Modern Relativity. The answer is about 0.994c.

I'll go look at it to better understand the dynamics, thanks.

...Ok I looked, unfortunately there are too many symbols I don't know; however the exact answer is helpful, thank you.

Maxila
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