relative speed?

I'm sure this isn't profound but I'd like to know the answer.
If two cars are going 55 MPH in opposite directions they are going 110 MPH relative to each other. In other words after an hour they will be 55 miles from their starting point and 110 miles from each other. Please no questions about what about when you go through a town etc /ubbthreads/images/graemlins/smile.gif. This is abstract.
Now if two space ships are going .8 C (the speed of light) towards each other are they approaching each other at 1.6 C ?

Question 2
If you are in a vehicle going 100 MPH and you shoot a projectile with a velocity that you observe to be 100 MPH does an outside observer see a projectile going at 200 MPH?
Most of you probably can guess the next question what do the afore mentioned ships observe (as well as an outside observer) if one shoots a laser at the other. BTW this is a low power laser not an opening salvo in a battle /ubbthreads/images/graemlins/smile.gif

wits'End,
Actually, every calculation involving relative speed is not supposed to be done in the example that you gave. There exist one equation that calculate the relative speed and it is not that simple. However, for speed much lower relative to the speed of light, the equation can be simplified through taking the limit and cancelling variables all over the place and come to the equation you use in the first example.
I believe the original equation involve something related to (1 + v^2/c^2)^(1/2) where V is your speed relative to the observer and C is the speed of light. When the v is much lower than c, the terms reduced to 1, which simplify things a lot.

the details on the equation is not handy to me right now. perhaps other member can chime in /ubbthreads/images/graemlins/grin.gif

So the closer we get to the speed of light the less observant we become? /ubbthreads/images/graemlins/twakfl.gif

Wits'End,

Yes. You have grasped the crux of the speed of light paradox. It gave the physicists at the turn of the century quite a bit of bother.

At speeds much lower than the speed of light ( 186,000 miles per second ) we have what is called Gallileon transformations, which is a simple straight forward vector addition. So two cars going opposite directions, each travelling 55 mph, are moving 110 mph relative to each other. If you shoot a 100 mph projectile from a 100 mph car, an observer standing on the side of the road sees it go 200 mph. Of course, even with these examples it is more complicated, because DIRECTION is critical. If we confine ourselves to "opposite" and "the same" directions, no problem. But what about a boat travelling across a river. There the velocity addition is with vectors at right angles to each other. Formally, Galilean velocity addition looks like this:

u = u' + v

where v is the velocity of, say, a train relative to the ground, u' is the velocity of a person relative to the train (walking around on the train, say) and u is the velocity of the person with respect to the ground. Instead of train and person you can substitute other fun examples, such as car w.r.t. ground, bullet w.r.t. car and bullet w.r.t. ground.

All of the things around is in everyday life travel at NON-relativistic velocities, except for light. In your laser beam example, the amazing things is that ALL observers, REGARDLESS of their relative motions measure the same speed for light, any light, all light.

For relativistic velocity addition, we must use the following very fun equation:

u = ( u' + v ) / (1 + u'v/c^2)

Clear as mud, right? If you'd like I can derive it for you /ubbthreads/images/graemlins/smile.gif

Recent experiments prove: The speed of light is relatively fast. /ubbthreads/images/graemlins/smirk.gif

Is 38 miles an hour fast? I guess it's all relative.
http://www.sciencedaily.com/releases/1999/02/990223083631.htm

Others say light has been slowing down since the universe was created. Has anyone timed it lately?
http://www.cbsnews.com/stories/2002/08/07/tech/main517850.shtml

Oh. I forgot. In the case of two .8c objects approaching each other, their relative velocity is:

(.8c + .8c ) / ( 1 + .8c*.8c/c*c )

or

1.6c/ (1 + .64)

or

1.6/1.64

or .9756c

i.e. 97 and 1/2 percent the speed of light relative to each other.

" ... ALL observers, REGARDLESS of their relative motions measure the same speed for light, any light, all light."

They all are limited to the same maximum observed speed, but their observed speeds can be lower as that is how lenses, prisms and gravatic bending work - slowing down light ...

[ QUOTE ]
Wits' End said:
...snip...
Most of you probably can guess the next question what do the afore mentioned ships observe (as well as an outside observer) if one shoots a laser at the other. BTW this is a low power laser not an opening salvo in a battle /ubbthreads/images/graemlins/smile.gif

[/ QUOTE ]

OK - The answer to this one is "Interesting", and you probably have 90% of the answer without knowing it

You've probably heard that time goes "Slower" as you approach the speed of light. There is a reason for this

Assume you are in a spaceship with a clock. Now an "Outside" observer says you are moving at 1/2C, BUT you say "I'm standing still, and the observer is moving"

When YOU turn on your laser, looking at YOUR clock, that laser beam will move away from you at C !!!! To the outside observer, the beam will move away from you at 1/2C !!!! How is this possible? Well, IF you could observer the two clocks (the one in the ship, the one the observer has), you will find that the clock in the ship is running exactly 1/2 as fast as the clock outside! (Which clock is right is "relative to your fram of reference") So, lets say the beam moves 186,000 miles from the front of the ship. A person inside the ship would say "1 second has elapsed". The outside observer would say "2 seconds have elapsed"

That is how the paradox is answered. It's the VERY non-intuitive thing that light in a vaccum moves at a constant speed. It's TIME that changes

The basic equation for speed is D = rXt . It is also expressed as r = D/t or t = D/r .
D = distance
r = rate of speed
t = time
c = the speed of light

It's interesting that the first assumptions to explain the "anomoly" was that D changed. Einstein postulated that it was t that changed.

Any two perspectives relative to a common phenomena possessing a rate approaching c exists in different time frames. Those time frames will differ in the manner necessary that the common phenomena will never exceed c, relative to each perspective.

[ QUOTE ]
Lara said:
Recent experiments prove: The speed of light is relatively fast. /ubbthreads/images/graemlins/smirk.gif

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rofl /ubbthreads/images/graemlins/yellowlaugh.gif

David <><

Empath,

D changes (or is relative to how the frames are moving w.r.t each other) as well !!! This is known as space contraction. Something moving near the speed of light is measured as shorter (a car or a train, for example) than it's rest length. What you really need are the Lorentz equations. They relate the position, time, and velocity of two events (x,y,z,t and x',y',z',t') in two reference frames in relative motion.

Thus, someone travelling near the speed of light experiences a shorter travel distance from point A to B, than what is measured in a frame at rest w.r.t. A and B. A beam of light experiences no distance at all between travel points, or you could also say that no time passes for it when compared to an outside observers clock. If you could ride a beam of light you could get anywhere in the universe in no time, BUT the universe will certainly age in that instant of your time, how much would depend upon how far you go.

Tomas,

Yes, I should have added " . . . in a vacuum" to the bit about the speed of light and relative observers.

Well I'm still confused but a whole lot less. The reminder about the time changing brought a whole lot back to mind.
THANKS!

I assume I'm missing something w/ this one
In the space ship example if the observer is outside the ships and observes them traveling towards each other.
The observer sees each ship going .6C how fast do they appear to be approaching each other? .9756C?
I'm doing my sig line again /ubbthreads/images/graemlins/frown.gif

Oh and the observer is using a Tachyon viewer to observe /ubbthreads/images/graemlins/grin.gif

Wits' End,

Your example was .8c not .6c, but whatever. Imagine an observer who sees each ship comming towards him such that they will both hit him and each other in a collision. Now the observer MIGHT see each ship approach him at 80 percent the speed of light, OR he might see one approach at greater than this and the other at less, but it's simpler if we assume he sees them both come at him at .8c. The pilots of the ships see each other approaching at .975c or whatever it was I calculated, and they see the observer approaching at .8c.

Now the observer might simply assume that the ships are approaching each other at 1.8c, but he would be wrong! If he sped up to keep pace with one of the ships, he would observe the other ships approach speed climb from .8c to .975c.

It's very odd isn't it? But remember that no one ever travels that fast relative to any other massive thing (like the earth), or is ever likely to do so. Even an astronaut in orbit doesn't travel nearly that fast, and he or she is going miles per second relative to the surface of the earth. We just don't have any experience with this stuff. If we were sub atomic or atomic particles then that would be different /ubbthreads/images/graemlins/smile.gif.

And in fact, small particles, such as electrons, act very strangely as they approach the speed of light. Here at Cornell's particle accelerator, our electrons or positrons are already moving at ALMOST the speed of light when they leave the first linear accelerator, at which point they have 300 million electron volts of energy. They have more than 10 times this energy after going through the synchrotron, yet they are still moving at ALMOST the speed of light. They actually SEEM as if they have more mass than they normally do! Also, they experience time at a slower rate. When you look at particle tracks in the detector and do a standard speed, distance, time calculation, it seems like a known particle which decays after a certain time, is actually lasting LONGER than it should. But really, it is that its time is NOT our time. Empath is right in saying that this was the key to Einstein's insight. He realized that we all simply assume that time is universal and uniform over all space and regardless of relative motion. But if you start thinking about how you would actually synchronize moving clocks, the puzzle will start to unfold itself.

The wierdest thing is that one persons space is another persons time! Take the lengh contraction. A moving car is measured as shorter by an oberserver at rest w.r.t the earth, let's say. Now suppose some hard headed practical person decided to show that it couldn't "really" be happening, by firing two high powered laser beams just in front and behind the "shortened" moving car. So that if the car were only apparently but not really shorter that it would get sliced by the laser, and the practical person could say, "see, it's not real." Here's what would happen: The person on the ground would see both lasers firing at once. The person in the car, however, would see the first laser go off just in front of his car, then, when the back of the car had moved past the second laser, he would see that laser fire just behind the car, and he would drive on unscathed.

So two events that are simultaneous in one reference frame (the observer on the ground), are not simultaneous in another (the person in the car).

OK. That's enough. People MUST be getting sick of this thread.

You want to know what relative speed is?....win the lottery! /ubbthreads/images/graemlins/hahaha.gif /ubbthreads/images/graemlins/grinser2.gif

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js said:
We just don't have any experience with this stuff. If we were sub atomic or atomic particles then that would be different /ubbthreads/images/graemlins/smile.gif.


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There is one relativistic effect that we do have experience with: electromagnetism.

asdalton,

Yeah! I actually did that calculation in modern physics. It's great fun. However, that's electrons in motion, LOTS of them in a wire, and NOT a bowling ball travelling at .8c, right?

Anyway, Maxwell's equations actually already were relativistically correct BEFORE Einstein's theory of special relativity. That's why the Lorentz transformations are called the "LORENTZ" transformations: because Lorentz derived them from Maxwell's E&M equations before Einstein derived them, but did not interpret them correctly. Maxwell's eq.s are invariant under a Lorentz transformation. That's how Lorentz derived those equations.

I read some articles a few months back that had two very interesting conclusions:
1. The speed of light is VARIABLE (several experiments in supercooled mediums. I believe the record was around 14mph!)
2. The speed of light is SLOWING DOWN. (mainly astronomical observations)

It seemed like legit stuff.