Headwrecking Relativity again.....

bonkey

Howdy all...

Ive been thinking about relativity and the speed of light (c) again, and Ive a conceptual problem that Im hoping someone might be able to clear up...

Heres the problem...

Lets imagine that we had the technology to accelerate spaceships to .6c.
Lets assume that we send spaceship A in one direction, and it accelerates to this speed at which point it just cruises along. This is no problem. Because the speed of the ship is less than c, all of our current models are satisfied, and there is no problem with communication.
Now, lets assume that we send spaceship B in exactly the opposite direction at exactly the same time. Thus the two ships are flying along a straight line, away from each other. B too accelerates to .6c and then cruises. Again, no problem.

But....

Relativity states that the speed of an object is relative to the observer. Thus, while both ships (A and are cruising, they would be observed as travelling at .6c from earth. However, if ship A tried to see what speed ship B is doing, we have a problem. Ship B is doing 1.2c relative to ship A.

This is a problem, because c is supposed to be an absolute limit.

Things get worse.....

Although ship B is travelling at speeds > c relative to ship A, there is no problem communicating between the two ships. Why? Well, because at the very least, A can relay a message to earth, which relays it on to B. At no time
is a message being sent between bodies travelling apart at speeds > .6c.

Things get worse....

Lets imagine that while the ships are flying apart, earth moves out of the way - which it will do being in an orbit and all.
Now, lets say ship A is at point a1, and it sends a single photon towards ship B at this time.
From B's perspective, a photon will be speeding towards it, at the usual speed (c) from a fixed point. But, ship B was moving away from a fixed point (earth) at a speed of .6c, and A1 is simply further away along the same line. Thus, its the same as if a signal was coming from earth...which is no problem.
Thus, although the ships are receeding from each other at 1.2c, it still seems possible that a beam of light (travelling at speed c) can bridge the gap!!!

This has been wrecking my head for days. And yes, Im aware how sad that probably makes me.

Im pretty sure that the time dilation effects of relativistic speeds will explain this away, but I cannot see how.

I especially cant see how it will work when these two spaceships launch probes in front of them, which accelerate up to .6c away from the ships, then cruise ahead at this speed. Now the relative speed difference between the probes is 2.4c, which means that an observer on one probe would, in effect, "see" the other probe travelling away from it at 2.4c. And so on to ever greater relative speeds, and yet without ever making communication impossible.

So...anyone well enough up on time dilation and/or relativity in general to explain to me where Ive gone wrong.....

Kev

The speed of A does not contribute to the speed of a photon leaving A as it would have with an object leaving A, so the speed of the photon relative to B is 0.4

or have i missed something ?

Kali

yep Kevs right.. any photons emitted from B towards A will be travelling from a fixed point at a speed of 1c towards A... when the light eventually catchs up with A (which it will.. as its going 0.4c faster) it will surely just appear as if B is at that fixed point (regardless of where B is now).

I don't see anything too complicated about that.. but like Kev said there may be missing something from my logic.

Repli

However, if ship A tried to see what speed ship B is doing, we have a problem. Ship B is doing 1.2c relative to ship A.

It wouldntt, light always travels at the same speed regardless of the motion of the observer,
if i was running towards you at 10km/h, and u were running towards me at 20km/h, your speed would be 30km/h relative to me, but light doesnt behave like this:

ship A would see ship B doing .6c

seamus

Yeah, I think everyone has it there. I have trouble with relativity too, particularly the limit on speed (ie. I'm going to need to see it proved before I fully believe it).

If a photon could leave ship A at .6c backwards, then it's travelling at the same velocity as ship B, not at 0c. That's theoretical....I dunno what happens if you slow down light. Anywho......So then if a photon of light leaves ship A at speed c, it will eventually catch up with ship B, because it's travelling .4c faster than ship B.

Best way I think of it is.....light moves so fast, that when a photon is emitted, the speed of the emitter at that microinstant in time, is 0, for all intents and purposes.
Of course, it's all theoretical. Essentially c is equivalent to infinity, ie. if a ship travelling at speed c, fires a rocket at speed c, then our gut tells us thatthe rocket is travelling at 2c. But relativity says it's travelling at c. Just like infinity......2 x infinity = infinity. So, where velocity is concerned, c acts like infinity......but c is measurable. Infinity is not. That's where I have a problem.......

bonkey

Originally posted by Kali
yep Kevs right.. any photons emitted from B towards A will be travelling from a fixed point at a speed of 1c towards A... when the light eventually catchs up with A (which it will.. as its going 0.4c faster) it will surely just appear as if B is at that fixed point (regardless of where B is now).

I don't see anything too complicated about that.. but like Kev said there may be missing something from my logic.

You can calculate speed by taking distance at two different points in time, and calculating the change in distance over time. You can calculate distance by bouncing a signal off the target (like radar does) and using the round trip time multiplied by the speed of your signal.

Example : I fire a signal at an object now, and estimate that it is X miles away (time for round trip * speed of light). One hour later I fire another signal, and estimate that it is Y miles away, I know that the object is travelling at (Y-X) miles per hour.

So....A launches a photon at B. It fires a second photon an hour later. B has a "reflector" which, when it receives the photon, sends one straight back with no time delay.

When A receives these two photons back, it can calculate the speed of B, relative to itself. All it does is calculate how far each photon travelled (how long it took * c) and get the difference.

Will it conclude that B is, indeed, travelling away from it at faster than the speed of light or not.

If it doesnt...then why not. What speed will it calculate?

jc

Kev

it should calculate that the relative velocity is 1.2 and the actual velocity is only 0.6

Woden

hi just read the first bit and as far as i know you can't just add the velocities like that to obtain 1.2c thats the original galilean transformations which only hold for velocities <<c

To the best of my knowledge the relative velocities between the two craft would be given by the additions of velocities formula derived from the lorentz transformations

the observed velocity on earth say V1 is given by

V1=(0.6c+0.6C)/(1+(0.6c*0.6c)/c^2)

which i calculate to be 1.2c/1.36=0.8824c < c as required

hope this helps

Data

Nietzschean

Originally posted by Dataisgod
hi just read the first bit and as far as i know you can't just add the velocities like that to obtain 1.2c thats the original galilean transformations which only hold for velocities <<c

To the best of my knowledge the relative velocities between the two craft would be given by the additions of velocities formula derived from the lorentz transformations

the observed velocity on earth say V1 is given by

V1=(0.6c+0.6C)/(1+(0.6c*0.6c)/c^2)

which i calculate to be 1.2c/1.36=0.8824c < c as required

hope this helps

Data

that is exactly correct, study this stuff in my course...
full lorentz transformations are for playing with..assuming motion in the x plane with velocity V

x = ã(x' + Vt')
y = y
z = z
t = ã(t' - (Vx'/c^2))
ã=(1+(V^2)/(c^2))^-1/2

if i recall without looking at me notes those are the main eqn's(lacking proper diag.'s to defn. it all fully but i'm not arsed drawing those for ye)...everything else can be derived from them. Newton's eqn's still stand but only in a a limiting case as can be seen that if V is alot less than c all the non standard terms become effectively 1 or 0 depending on equasion.

anything else ask away...we bugged our lecturers for ages with all these questions.

Nietzschean

Originally posted by seamus
Yeah, I think everyone has it there. I have trouble with relativity too, particularly the limit on speed (ie. I'm going to need to see it proved before I fully believe it).

If a photon could leave ship A at .6c backwards, then it's travelling at the same velocity as ship B, not at 0c. That's theoretical....I dunno what happens if you slow down light. Anywho......So then if a photon of light leaves ship A at speed c, it will eventually catch up with ship B, because it's travelling .4c faster than ship B.

Best way I think of it is.....light moves so fast, that when a photon is emitted, the speed of the emitter at that microinstant in time, is 0, for all intents and purposes.
Of course, it's all theoretical. Essentially c is equivalent to infinity, ie. if a ship travelling at speed c, fires a rocket at speed c, then our gut tells us thatthe rocket is travelling at 2c. But relativity says it's travelling at c. Just like infinity......2 x infinity = infinity. So, where velocity is concerned, c acts like infinity......but c is measurable. Infinity is not. That's where I have a problem.......

well as quoted above the end of your logic is flawed, and just for the record this stuff has mostly been observed if not entirely proved at cern and using high speed jets for time dialation.

a few things :
1) By Einsteins second law thingy no matter what your refrence frames relitive motion to the light source the speed of light will always be measured as c. i.e moving at a light source at speed .99999c you will still measure the speed of light as c.

2) from 1 light cannot be slowed down as such and above firing a proton backward at .6c will just give it a velocity of -.6c relitive to the inertial frame that A is in , i really don't see how this one causes a problem, this one is visible from newtonian mechanics....... relative to ship B this proton is not moving as it has no relative velocity to it i.e equal relative velocity w.r.t A

3) as someone mention'd at some stage about moving earth, there is no such thing as a fixed point per say when one does special relativity, everything is relative to inertial frames, i.e. earth is in its own inertial frame which means from its perspective everything else moves around it, the same applies to all the problems above, none of them actually view themselves moving per say, they only view the relative motion of the other objects toward or away from them.