Thread: Another speed of light question !?

Hi guys, just when I'm beginning to think I'm understanding a bit more, a simple example tends to throw me ! For instance, regarding the speed of light I understand that light travels at 186.000 miles a second, nothing can travel faster than light. But what if we could in fact send a signal faster than the speed of light ? I read this as an example,

someone shoots you with a gun, but you send a signal faster than the speed of light and backwards in time to the gunman, this signal could stop the person pulling the trigger that shot the bullet that has already hit you. !?

I get a flash in my brain now and again illuminating some understanding of this statement but then the light goes out and I'm not understanding it at all !

Can you explain the validity or otherwise of this statement ?

BARCUD

You seem to be trying to disprove a certain thing - c being the fastest anything can travel - by postulating a situation where c is not the limit. So I don't understand the logic of what you are asking. It's as if you said "All swans are white, but suppose I had a blue one, how could that be?"

Perhaps I have misunderstood you.

I must agree with john. I too am having the same difficutly in understanding your problem. Nothing may travel faster than light, mainly because doing so would require an infinite amount of energy.

However, there are particles postulated to go faster than light, called tachyons. no evidence has ever been found of their existence though, so I personally do not believe that they exist.

We need to clarify what a "thing" is. Is a hot spot on a wall a thing? Then wave a laser at a wall: that "thing" on the wall may race along faster than light. You could make that "thing" shaped like a three dimensional snail or whatever.

Also if I'm not mistaken the rule only says no thing can accelerate beyond the speed of light. So if by nature that thing exists only at FTL speeds, no problem.

I'm taking a different view of your question here and simply going to say "Yes".

The speed of light helps define not just our understanding of time, but also the 'cone of time', beyond which we have no access to information.

If, therefore, you could travel faster than light (considered primarily a science fictional notion even amongst speculative physicists) then you would, in effect, be travelling backwards in time and could violate causality.

When you start thinking in those terms, however, physics is no longer your friend and you are best off reading science-fictional works on time loops, causality and time travel paradoxes.

Also if I'm not mistaken the rule only says no thing can accelerate beyond the speed of light. So if by nature that thing exists only at FTL speeds, no problem.

I'm not quite sure about that. I have a copy of Einstein's original paper here and he quite clearly says nothing may go faster than light.

If, therefore, you could travel faster than light (considered primarily a science fictional notion even amongst speculative physicists) then you would, in effect, be travelling backwards in time and could violate causality.

Absolutely true.

Also, going faster than light would mean having negative energy. This is because applies only to particles at rest. In motion this is



It should be obvious that any velocity faster than light here would result in a negative number. Multiplying that negative number with , we get negative energy.

By the way ... isn't it striking that Dirac postulated the existence of positrons (anti-electrons) by interpreting a negative energy as a representative for anti-particles? And in fact, in a Feynman diagram, a positron looks like an electron travelling back in time.



I think, there is even a hypothesis that there might only be one electron in the universe, and all electrons and positrons that we see are actually one and the same particle.

Originally Posted by Dishmaster

I think, there is even a hypothesis that there might only be one electron in the universe, and all electrons and positrons that we see are actually one and the same particle.

I thought that was for photons. No?

Hi guys, I'm causing more confusion than I am confused !

My question above may best be described as 'philosophical' ? It refers to the question 'what if ?' something could travel faster than light. Anything travelling up to the speed of light could be said to have 'ordinary energy', and anything travelling beyond the speed of light would involve 'negative energy' ? Would objects then be travelling backwards in time ?

Of course I may well be reading this all wrong but you can read what I am refering to in Nigel Calders 'Einsteins Universe', p.132.

So, anything up to the speed of light is physics and beyond that we travel into the realms of philosophical questions or science fiction ?

BARCUD

Originally Posted by Dishmaster

I think, there is even a hypothesis that there might only be one electron in the universe, and all electrons and positrons that we see are actually one and the same particle.

This too, I believe, was initiated as a thought by the great Feynman.

And Barcud, yes: up to the speed of light is physics and beyone is philosophy and speculation (and most physicists are quite happy to speculate in this manner - they're fun and exciting thoughts, after all, but they'll not, if they're any good, claim it as hard science).

Okay thanks guys,

SO WHAT IF . . . we fire off a beam of light AND at the exact moment we fire off another beam (yet to be discovered ) that travels faster than the beam of light ?

Which beam would reach our imagined destination first ? In theory it would be our fictional beam S0 . . . wouldn't that beam actually be going FORWARDS in time and not backwards ?? Will it not have reached a place in the future which the beam of light has yet to reach ??

BARCUD

I am going to end this right now. U cant go faster than the speed of light because u get negative energy and u would reach critical mass and everything would be destroyed etc.

Originally Posted by BARCUD

Okay thanks guys,

SO WHAT IF . . . we fire off a beam of light AND at the exact moment we fire off another beam (yet to be discovered ) that travels faster than the beam of light ?

The thing is that the properties of space "govern" how fast light can travel, it really has little to do with light itself.

the vaildidation of this idea lies in the wording
traveling faster than the speed of light wouldnt make you go back in time,
it would let you reach the future faster than everyone else
if you've already been hit theres nothing you can do about it

Originally Posted by the man of science

I am going to end this right now. U cant go faster than the speed of light because u get negative energy and u would reach critical mass and everything would be destroyed etc.

Would you show us the math please.

for critical mass? IDK

Originally Posted by the man of science

for critical mass? IDK

Then why did you make the statement? You were quite definitive that you were going to end this right now. That degree of certainty can only come with math. So, perhaps you were rather overstating your case. Yes?

Well yeah. Its impossible to find an equation for critical mass.

Originally Posted by the man of science

Well yeah. Its impossible to find an equation for critical mass.

Would you like to define critical mass in this context?

As speed increases so does mass. At the speed of light the mass is so huge that it can't contain itself and implodes causing a massive destabilization and destruction of the universe.

Originally Posted by the man of science

As speed increases so does mass. At the speed of light the mass is so huge that it can't contain itself and implodes causing a massive destabilization and destruction of the universe.

You still haven't defined critical in this context. Would you do so please?

How huge is the mass?
Why can't it contain itself?
(If it implodes, surely cannot contain itself is a very misleading phrase - an implosion is very much an act of containment, is it not?)
Why would this destroy the universe?

argh!! Do I look like a physicist? I can't explain too much more than I already have without looking on wikipedia for more detail to be honest. An implosion occurs when the forces within the object are so great that it rips itself apart.

"Critical masss is the smallest amount of fissile material needed for a sustained nuclear chain reaction."

Now as for traveling faster then light, I believe it has already been proven that Electrons in Fission reactions are ejected at faster then the speed of light causing Cherenkov Radiation. In sense these should be called Tachyon Electrons.

http://en.wikipedia.org/wiki/Cherenkov_radiation

Sending a signal back in time is covered in the Tachyon Antitelephone.

http://en.wikipedia.org/wiki/Tachyonic_antitelephone

Originally Posted by the man of science

argh!! Do I look like a physicist?

No you don't. And I think when you posted this statement "U cant go faster than the speed of light because u get negative energy and u would reach critical mass and everything would be destroyed etc" you were mainly waffling.

I have nothing against waffle. It can be very entertaining, but I think it is out of place in a serious discussion on a science board.

Tharghana has supplied the only definition of critical mass I am familiar with and a I fail to see how it relates in any way to FTL travel.

I wasn't waffling. What I said is correct, but like I said, I don't know too much about this subject as it is pretty abstract.

Maybe People Should read my quite Relevant Post instead of blathering on about waffling.

I did and ur right too. U added to what I had already stated and cleared up some stuff.

Man of science,
this is my last post in response to one of yours for a little while. It is becoming ridiculous. Your posts are either so general that waffle is the best descriptor, or - when they are precise - they tend to be wrong.

Here's another example, you describe an implosion thus - "An implosion occurs when the forces within the object are so great that it rips itself apart."
That is quite simply wrong. The whole point about an implosion is that it is a collapse in which the object is condensed inwards, the very opposite of 'ripping itself apart'.

I now expect something from you along the lines of 'Well yes, but the object is destroyed and that's what I mean by being ripped apart." Or you'll politely say "Yes, ur right." But you will still proceed, in the next sentence to utter another piece of nonsense.

Anyway, I'm getting tired of correcting you. You are probably getting tired of being corrected. I make a final appeal to you - think before you post.

You should really know by now that the man of science's post are 50% bullsh**.
If you go to every thred he posted in, there will be always someone correcting him so you should just ignore him.

You should really know by now that the man of science's post are 50% bullsh**.
If you go to every thred he posted in, there will be always someone correcting him so you should just ignore him.

shut up mr.yang. Don't ignore me because I am right 90% of the time. Stop hating on me because ur jealous people. If u think I am so stupid then ask me some questions Yang. Prove to me that ur smarter than me which I highly doubt that u can.

If I may butt in, I think man of science meant infinite mass, instead of critical mass. A small mistake, but the difference is enormous.

Moreover, infinite mass at the speed of light is correct. This can be explained as so:

The Einsteinian equation for relative mass is this:



By the way, I apologise if I have written this down incorrectly; it has been quite some time since I've had to remember it.

As can be seen by the above, when the velocity is directly equal to the speed of light, the Lorentz factor comes to be zero, and we all know that any value divided by zero becomes infinite.

So, man of science's premise that at the speed of light, infinite mass would be achieved is correct.

Yeah srry. I looked up critical mass on dictionary.com and Thargana's definition was correct. I also looked up infinite mass which matches the definition I was expressing. Srry for the mix-up there.

Originally Posted by Liongold

So, man of science's premise that at the speed of light, infinite mass would be achieved is correct.

Correct, but his sloppiness in the use of terms meant that he maintained that small mistake with an enormous difference throughout the thread. This was despite me asking him a number of questions that should have helped him recognise his error. Instead he launched into inadequate, distorted general explanations that added nothing to the discussion. Nor do I think his follow on premise that this condition would 'destroy everything' has much basis in physics.

Liongold, I think you are trying to do a noble thing here: keep the discussion going, clarify points with solid mathematics, and be positive about the contributions of all posters. I've just reached the conclusion that man of science needs a good kick up his backside so that he can properly realise his potential.

Just an opinion. :wink:

Originally Posted by Liongold

If I may butt in, I think man of science meant infinite mass, instead of critical mass. A small mistake, but the difference is enormous.

Moreover, infinite mass at the speed of light is correct. This can be explained as so:

The Einsteinian equation for relative mass is this:



By the way, I apologise if I have written this down incorrectly; it has been quite some time since I've had to remember it.

As can be seen by the above, when the velocity is directly equal to the speed of light, the Lorentz factor comes to be zero, and we all know that any value divided by zero becomes infinite.

So, man of science's premise that at the speed of light, infinite mass would be achieved is correct.

A couple of nits to pick.

The correct expression is



division by zero does not equal infinity, but is rather undefined.

So while one could say that the relativistic mass approaches infinity as v approaches c, you can't say that it equals infinity when v=c.


That being said, the term "relativistic mass" has even become passe in scientific circles. This probably a good thing seeing how it tends to lead to some confusion among lay-people (such as the idea that an object will be crushed by its own mass as it approaches c.)

Instead, mass is now considered invariant and only refers to the rest mass. "Relativistic mass" is simply termed "energy". as in the increased Kinetic energy of the mass in question .

Thus a better explanation is to say that the kinetic energy of a mass approaches infinity as v nears c as per the following equation.



Another way of explaining the c speed limit is through the addition of velocities theorem:



Example, assume you have space ship traveling at 0.5c relative to an observer.

The spaceship drops a buoy and then accelerates away from it at 0.5c in the same direction as the relative motion it already has with respect to the observer.

Using non-relativistic velocity addition, you would expect the ship to now have a relative speed of 0.5c+0.5c= 1c with respect to the observer.

Instead, he ends up with a relative speed of



In other words, even though the buoy still moving at 0.5c relative to the observer, and the ship moving at 0.5c relative to the buoy, the ship is only moving at 0.8c relative to the observer.

The ship can try it again; dropping a new buoy and accelerating away at 0.5c. After which the ship will be moving at 0.5c relative to the second buoy, at 0.8c relative to the first buoy, and




Relative to the observer. No matter how many times the ship does this, it will never reach a speed of c relative to the observer. It will closer and closer, but never quite get there.

Very interesting Janus! A few questions. From the ships own perspective, how would it be able to know at what fraction of C it is travelling? Maybe by the relation between inertia induced pseudo gravity to the amount of energy expended? Would they even be able to measure it reliably, or do they inescapably have to measure their velocity relative to something else?

Would it be accurate for me to summarise what happens by saying that the greater V becomes, the more of the energy expended goes toward increasing inertia and less towards increasing velocity in a way exactly predicted by relativity? So some mechanism we have no clue about causes this to happen in this way, or do we have some kind of an idea?

There is in general no problem with negative energy. For example we often place gravitational potential energy at zero out at infinity and all finite locations have a negative gravitational potential energy.

The total partical energy equation that has be used in this post is wrong. It should be:


Now you see that to even go the speed of light would take an infinite about of energy. The only "things" that can go the speed of light are massless partials like the photon and the graviton.

Originally Posted by c186282

The total partical energy equation that has be used in this post is wrong. It should be:

oops! I must not have refreshed my browser. I see others have gotten the correct equation before me.

Originally Posted by c186282

There is in general no problem with negative energy. For example we often place gravitational potential energy at zero out at infinity and all finite locations have a negative gravitational potential energy.

The energy equation however produces the square root of a negative number, an imaginary number, for values of v over c

The total partical energy equation that has be used in this post is wrong. It should be:

The equation I gave was for the Kinetic energy alone, which is the total energy minus the energy equivalence of the rest mass.

The total energy equation can be expanded to the series:



Where the first term is the rest mass energy equivalence.

Now you see that to even go the speed of light would take an infinite about of energy. The only "things" that can go the speed of light are massless partials like the photon and the graviton.

Did people fail to read my post, of just not take notice to it?

[quote="Janus"]The energy equation however produces the square root of a negative number, an imaginary number, for values of v over c[quote]

Yes of coarse. My comment on negative energy was just to point out that there is nothing strange about the idea of negative energy in general. Often I have used negative potential energy in solving problems.

Now imaginary energy that is a poor concept. If someone was selling me some imaginary energy I would keep a close eye on my wallet.

Originally Posted by Tharghana

Did people fail to read my post, of just not take notice to it?

From your link:

"Čerenkov radiation (also spelled Cerenkov or Cherenkov) is electromagnetic radiation emitted when a charged particle (such as an electron) passes through an insulator at a speed greater than the speed of light in that medium."

We are discussing the speed of light in a vacuum, which is C. The speed of light through a medium is less due to the time taken up by the absorption/emition of the photons by the constituent compounds of the medium.

Tachyons are hypothetical particles whose possibility are not ruled out by Einstein's equations AFAIK, but have never been observed. They work differently, in that they travel at C when infinite energy is applied, but when less than infinte energy is applied it travels at speeds exceeding that of light and at infinite speed when none is applied. AFAIK

In Theory, you could have a particle go faster then light in space, because space inst a true Vacuum, a few stray hydrogens are out there.

Originally Posted by KALSTER

"Čerenkov radiation (also spelled Cerenkov or Cherenkov) is electromagnetic radiation emitted when a charged particle (such as an electron) passes through an insulator at a speed greater than the speed of light in that medium."

Well done, in that medium is key!

Originally Posted by Tharghana

In Theory, you could have a particle go faster then light in space, because space inst a true Vacuum, a few stray hydrogens are out there.

It doesn't work that way. the hydrogen atoms in interstellar space are just too spread out to act as a medium for light.

This is demonstrated as follows:
The amount a medium slows light is determined by its index of refraction. The index of refraction for any material differs for different frequencies of light, thus different frequencies are slowed by different amounts when passing through a medium.

If interstellar or intergalactic space acted as such a medium, then we would receive the different frequencies of light from an event occurring in deep space(say a Supernova in a distant galaxy spread out over a time span.
We don't, all the frequencies of light from the event arrive at the same time, meaning none of the light was delayed by interaction with a refractive medium.

Cool. Now, is my question next? :wink:

Originally Posted by KALSTER

Very interesting Janus! A few questions. From the ships own perspective, how would it be able to know at what fraction of C it is travelling? Maybe by the relation between inertia induced pseudo gravity to the amount of energy expended? Would they even be able to measure it reliably, or do they inescapably have to measure their velocity relative to something else?

All velocities are relative. So yes, they have to measure velocity with respect to something else. IOW, there is no experiment or measurement they can make that will determine some absolute motion

Would it be accurate for me to summarise what happens by saying that the greater V becomes, the more of the energy expended goes toward increasing inertia and less towards increasing velocity in a way exactly predicted by relativity? So some mechanism we have no clue about causes this to happen in this way, or do we have some kind of an idea?

As viewed by a observer that measures the object's velocity as V, then yes. Or another way to look at it is that energy itself carries its own inertia. So as you add energy to an object you are also adding inertia, which then takes even more energy to overcome, which adds its own inertia...

The other way is to realize that energy is measured in units of mass-distance²/time², and since relative velocity effects measurements of distance and time, it also effects energy. (the Energy formulas given above were derived from the time dilation and length contraction formulas.)

All velocities are relative. So yes, they have to measure velocity with respect to something else. IOW, there is no experiment or measurement they can make that will determine some absolute motion

This relates to Newton's bucket thought experiment, no? If a space ship with no windows were alone in space and fired its engines, would the occupants not notice the inertia of acceleration? Would the water in the bucket not stay in the bucket?

Or another way to look at it is that energy itself carries its own inertia.

Would it then be accurate to say that inertia is the absolute measure of mass? I mean like in the case of nuclear isomers. They have increased mass and inertia, but consist out of the same fundamental particles as a regular nucleon of the same element, no?

I realise that the increased inertia of an accelerating mass would only be from a relative observer, but has this been directly observed? For instance, would particle accelerators have different results if this were not the case?

PS: If you think I should open a new topic for this, I'd be happy to or you could do the honours, if you feel so inclined, with my blessing.

SO WHAT IF . . . we fire off a beam of light AND at the exact moment we fire off another beam (yet to be discovered Smile ) that travels faster than the beam of light

Well, in a medium, two beams of light of different energies and therefore frequencies will travel at different speeds. The first beam of light will actually limit the second beam of light and prevent it from passing it......there was an article about this a few months ago that I discussed here, I believe it was called, "The gate of no return" and quoted Dante's Inferno at some point.

Example, assume you have space ship traveling at 0.5c relative to an observer.

The spaceship drops a buoy and then accelerates away from it at 0.5c in the same direction as the relative motion it already has with respect to the observer.

Using non-relativistic velocity addition, you would expect the ship to now have a relative speed of 0.5c+0.5c= 1c with respect to the observer.

Instead, he ends up with a relative speed of

\frac{0.5c+0.5c}{1+\frac{0.5c(0.5c)}{c^2}}= 0.8c

In other words, even though the buoy still moving at 0.5c relative to the observer, and the ship moving at 0.5c relative to the buoy, the ship is only moving at 0.8c relative to the observer.

The ship can try it again; dropping a new buoy and accelerating away at 0.5c. After which the ship will be moving at 0.5c relative to the second buoy, at 0.8c relative to the first buoy, and

\frac{0.5c+0.8c}{1+\frac{0.5c(0.8c)}{c^2}}= 0.92857c

Hmm...this is the explanation that I have been looking for as to why we cannot bring things in a particle collider faster than c. Though....I think I am more confused now.

What you stated.....is extremely strange.......what sort of dynamic controls this?

Before I end up spending hundreds of hours trying to figure this out, I have to know; do we know as a fact that this is true?

Say....the space ship dropped a buoy at .1c relative to the observer, then accelerated .7c relative to the buoy...how fast will it be moving relative to the observer? I would do the calculation but for some reason my calculator will not do it (Its a TI-84 Plus SE). What I want to know is, does the unlinearity only occur when going at or exceeding c by adding each relative velocity together?

No....that would not be possible....to suddenly have .5 + .5 = .8, when just before, .5 + .499999999 = 9.99999999.

I am bad at math and cannot properly analyze the equation yet......is there any point where the addition is linear? Should I assume it becomes more linear the lower the two numbers added together?

Does anyone understand how this works? It is a little beyond me right now....

Originally Posted by Cold Fusion

Hmm...this is the explanation that I have been looking for as to why we cannot bring things in a particle collider faster than c. Though....I think I am more confused now.

What you stated.....is extremely strange.......what sort of dynamic controls this?

Before I end up spending hundreds of hours trying to figure this out, I have to know; do we know as a fact that this is true?

Yes we do. It is a straightforward result, as I understand it, from Einstein's Special Thoery of Relativity, and has been demonstrated in practice. Bear in mind that a lot of these demonstrations have been by way of indirect meaurements: we currently have no way of accelerating anything but nuclear particles to those speeds and unfortunately, have no way of fixing speedometers to them, so have to draw conclusions by inference from their behaviour.

What I want to know is, does the unlinearity only occur when going at or exceeding c by adding each relative velocity together?

The so-called non-linearity occurs at any speed. At low speeds, however (low compared to the speed of light in a vacuum), they are so small as to be negligible - effectively beyond the capacity of our instruments to measure.

..............from what I can tell (as for the first part, whereupon only one buoy has been dropped).....the .8c is the absolute speed, the "true" speed. So....we still have the buoy moving .5c away from the observer and the spaceship moving .5c away from the buoy. If this is true, then to maintain this 1:1 ratio, the buoy must never gain any relative distance on the space ship, and change the distance ratio from the observer being x away from the buoy, and the buoy being x away from the spaceship....any gain on the spaceship would turn one of the x's into .000000000001x and so forth, breaking the 1:1 ratio.

So even though the space chip is moving .8 relative to the observer, and the buoy is going .5, the spaceship must accelerate away at .5c, not .3c

This is assuming the velocities are absolute, and not virtual or perceived to be that way....is that correct?

When you say something is traveling, say a car, 50Kmh slower then a car traveling at 100Kmh, it must be moving at 50Kmh.....still a speed, because a speed is allowable here....but if you say that the car is traveling 50Kmh slower then something traveling 0Kmh....then it must be moving -50Kmh. Regardless of the fact that it us traveling -50Kmh, the first car is still traveling in essence 50Kmh faster then it? And if you wish...you could say that instead of you moving backwards, and it standing still, YOU are standing still and it is moving at 50Kmh. So you are able to convert a negative to a positive through a relativistic switch in perception.....making either statement true and valid.

In other words.....either the spaceship is moving .5c relative to the buoy in the forwards direction, or the buoy is moving relative to the spaceship, -.5c, therefore in the backwards direction. Your observer is standing still with the buoy moving at .5c, or the buoy is standing still and the observer is moving backwards.

Just some ramblings............well, what I would like to know is.........if you magically attached a string to the observer and the buoy, then between you and the buoy, then between you and the observer at say, 5 minutes after you start away from the buoy at .5c, and you made the length of the string from you to the observer the same length as the combined length of the one from the observer to to the buoy and from the buoy to you, would your string sag, would it be taught, or would it reach you at all? :?

Originally Posted by Cold Fusion

..............from what I can tell (as for the first part, whereupon only one buoy has been dropped).....the .8c is the absolute speed, the "true" speed.

There ain't no such thing, I'm afraid.

The only speed you can measure is speed relative to you. To you, therefore, no matter how fast or far away you think you are moving, the relative speed of another object (apart from the massless photons etc) will always be less than that of light.

The equations on this thread simply show how, in principle, you can calculate what that perceived speed will be.

Thinking about 'absolute' speed is a conceptual trap and will hinder your appreciation of relativity.

Originally Posted by Cold Fusion

Say....the space ship dropped a buoy at .1c relative to the observer, then accelerated .7c relative to the buoy...how fast will it be moving relative to the observer? I would do the calculation but for some reason my calculator will not do it (Its a TI-84 Plus SE). What I want to know is, does the unlinearity only occur when going at or exceeding c by adding each relative velocity together?

No....that would not be possible....to suddenly have .5 + .5 = .8, when just before, .5 + .499999999 = 9.99999999.

I am bad at math and cannot properly analyze the equation yet......is there any point where the addition is linear? Should I assume it becomes more linear the lower the two numbers added together?

Does anyone understand how this works? It is a little beyond me right now....

as already pointed out, it never becomes perfectly linear, it does come close when using small velocities.

for instance adding 0.001c to 0.001c gives 0.001999998c

Originally Posted by Cold Fusion

Hmm...this is the explanation that I have been looking for as to why we cannot bring things in a particle collider faster than c. Though....I think I am more confused now.

What you stated.....is extremely strange.......what sort of dynamic controls this?

The same dynamic that give us time dilation, length contraction, and the Simulataneity of Relativity, the fact that Light travels at the same speed relative to any observer and measured by that observer.


For example, you have a spaceship with a clock in the tail and a clock in the nose. In the Spaceship's frame, these clocks read indentical times. If you fire a bullet from the tail of the ship to the nose, an observer will find the velocity of the bullet realtive to the ship by taking the difference between the reading of the tail clock when the bullet was fired and the reading on the nose clock when the bullet arrives, and dividing it into the length of the ship.

Now imgine you are an observer outside of the ship and the ship has a relative motion to you. The bullet is fired just as the tail of the ship passes you. You have a clock next to you and a bunch of clocks strung out along the path of the ship, each in snyc with yours. You can caluculate the bullet's relative velocity to you by taking the difference between your clock and the clock the nose of the ship passes the instant the bullet reaches the nose, and dividing that into the distance between you and that clock.

Now here's the tricky part:

The clock in the nose of the Ship must show the same reading when the bullet reaches accirding to both the person in the ship and the outside observer.

According to the outside observer, the clocks in the ship run slow.
According to the outsdie observer, the ship is length contracted, and the distance between the tail and nose is shorter.
According to the outside observer, the nose clock and tail clock do not show the same time at any given instant (the Nose clock lags behind the tail clock.)

Once you take this all into account you end up with the formula for velocity addition I gave eariler for determining the velocity of the bullet with respect to the outside observer.

Wait.....so you are saying the buoy moving at .5c can only see the ship moving .5c faster because it is length contracted and therefore will measure it under those influences and receive a different reading? while in reality it only accelerated .3c relative so someone who is not undergoing the effects of length contraction and time dilatation.

If this is so, then I guess I will not have to continue the (I'm not sure how to label it) vector eigenvalue multi dimensional state theory I was working on....

Originally Posted by Cold Fusion

Wait.....so you are saying the buoy moving at .5c can only see the ship moving .5c faster because it is length contracted and therefore will measure it under those influences and receive a different reading? while in reality it only accelerated .3c relative so someone who is not undergoing the effects of length contraction and time dilatation.

Nobody "undergoes" the effects of Length contraction nor Time dilation. Not in the sense you are using, where person A "undergoes" length contraction and this effects his prerception of the Universe. Instead, you measure Length contraction and Time dialtion as happening to objects that have a relative motion with respect to you. IOW, relativistic effects always happen to the "other guy".
All the velocities measured are "real".

Imagine three points A,B and C placed on the arc of a circle. There is a straight line distance between A and B and Between B and C, which are the real distances between these points, but the straight line distance between A and C is not just the addition of the straight line distance's A-B and B_C, even though B is between A and C on the Arc. The same kind of thing applies to the addition of velocities.

[quote]

....I actually drew what you explained to try to understand this ; )

If that is true and it does not just appear that the ship is moving away at .5c, but IS moving away at .5c, then I am once again totally confused as to how that is possible. Janus, did you teach yourself this? Relativity is killing me.....more so then QM.

The most important thing to remember is that the speed of light is independent of the inertial frame it is seen from. The phenomena of time dilation and length contraction are a fairly simple result of this fact that can be explained with a Pythagorean triangle.

http://hyperphysics.phy-astr.gsu.edu...ativ/tdil.html
http://www.phys.unsw.edu.au/einstein...e_dilation.htm