Chasing light speed

Carl · #1 20-08-2008, 07:45 PM

This will sound stupid but I'm no Astro Phyisist (or Speller)
I woke up thinking this last week and no one has answered it yet and I'm looking for a simple explination.

I'm being chased by an enemy space ship. We are both travelling at the speed of light and for arguments sake we are 500m apart.The enemy turns their headlights on to see me better (it's dark out in space).

Question 1. Will the beam of light catch up to my ship, does the light travel at the speed of light plus the speed of the ship?

Question 2. When i look back at the enemy ship will I see the headlights?

Question 3. The enemy is carrying a standard issue rifle that shoots a bullet at approx 4500ft per sec. Will the bullet hit me. Is the bullet travelling at light speed plus the velocity of the bullit or only at the speed of the bullet.

Is the above the same principle as throwing a ball forward in a train or does it all change in space and at light speed?

Do the headlights and bullet theoretically travel faster than the speed of light?

I'm just a mug backyard astronomer but I cant get this off my mind an it's anoying the people i work with.
can anyone explain in plain English.

Regards
(not so bright)Carl

Babalyon 5 · #2 20-08-2008, 09:28 PM

Wow! Cool dream! You musta done really pissed of those aliens!

Cant wait for the answers to this one!!

Zuts · #3 20-08-2008, 11:16 PM

Hi,

Question (1), the beam of light will be travelling at the speed of light so in your spaceship yes it will catch you up at the speed of light.
Question (2), particles with mass cannot travel at the speed of light. Regardless, adding the velocities of any two objects with a velocity less than the speed of light will always give an answer less than the speed of light, no matter how close to the speed of light the objects are.

The formula for adding relativistic velocities is quite straightforward, it is

w = (u+v)/(1+ uv/c2), where c is the speed of light, u, v are the velocities to be added.

(1) Plugging in the values for everyday speeds then it is roughly u + v as uv/c2 is very small. So this agrees with everyday observation.
(2) if u and V are both c, the speed of light as in your first question then plugging in the values you get c. So this agrees with the fact that the speed of light is a constant for all observers.
(3) your second question is not quite right. Bullets cannot travel at the speed of light. Anything with mass can only approach the speed of light. Plugging in values approaching the speed of light will always give a value less than the speed of light which agrees with the fact that particles with mass can never travel faster than the speed of light.

Cheers
Paul

GTB_an_Owl (Geoff) · #4 21-08-2008, 12:09 AM

Hi Paul

i have to question your answer to Q1
if A and B are both travelling at the speed of light and A is 500 metres in front of B, the light from B will never catch A.
to my mind it will always be 500 metres behind A ?

and i would love to be in ship A - cause i could shoot B - but B could not shoot me

geoff

AdrianF (Adrian) · #5 21-08-2008, 07:55 AM

I think it is all relative. The light from the headlights would catch up to your craft because the light would travel at the speed of light relative to your speed.
The rifle I have a little trouble with, because the projectile is travelling much slower than the speed of light the bullet would leave the end of the barrel (speed of light + 4500f/s, relative 4500f/s) but as the projectile slows (would it?) the aliens would be in danger of shooting themselves as they overtake the projectile.
Forgive the ramblings of a sick man (bloody flu)

Adrian

sjastro · #6 21-08-2008, 09:23 AM

Quote:

Originally Posted by Carl

This will sound stupid but I'm no Astro Phyisist (or Speller)
I woke up thinking this last week and no one has answered it yet and I'm looking for a simple explination.

I'm being chased by an enemy space ship. We are both travelling at the speed of light and for arguments sake we are 500m apart.The enemy turns their headlights on to see me better (it's dark out in space).

Question 1. Will the beam of light catch up to my ship, does the light travel at the speed of light plus the speed of the ship?

Question 2. When i look back at the enemy ship will I see the headlights?

Question 3. The enemy is carrying a standard issue rifle that shoots a bullet at approx 4500ft per sec. Will the bullet hit me. Is the bullet travelling at light speed plus the velocity of the bullit or only at the speed of the bullet.

Is the above the same principle as throwing a ball forward in a train or does it all change in space and at light speed?

Do the headlights and bullet theoretically travel faster than the speed of light?

I'm just a mug backyard astronomer but I cant get this off my mind an it's anoying the people i work with.
can anyone explain in plain English.

Regards
(not so bright)Carl

From the frame of reference of the spaceships, the questions have no meaning if it was possible to travel at the speed of light (which it isn't). Both spaceships and the distances they travelled would be length contracted to zero. There would be simply be no spatial dimension in the direction of motion for both spaceships. The spaceships would behave as photons.

The speed of light from the cars headlamps is constant irrespective of whether the car is in motion or not. Additive velocities don't apply to light.

Regards

Steven

Karls48 (Karl) · #7 21-08-2008, 10:22 AM

Quote:

Originally Posted by sjastro

From the frame of reference of the spaceships, the questions have no meaning if it was possible to travel at the speed of light (which it isn't). Both spaceships and the distances they travelled would be length contracted to zero. There would be simply be no spatial dimension in the direction of motion for both spaceships. The spaceships would behave as photons.

The speed of light from the cars headlamps is constant irrespective of whether the car is in motion or not. Additive velocities don't apply to light.

Regards

Steven

Travelling at speed of light - Relative to what? The Earth, some distant galaxy receding from the Earth faster then speed of light or centre of the universe?
If Big Bang theory is correct the only meaningful measurement of time, motion and distance is referencing it to the point in the universe where the Big Bang occurred, (and the time and space come to existence).

JohnH · #8 21-08-2008, 11:57 AM

Quote:

Originally Posted by Karls48

Travelling at speed of light - Relative to what? The Earth, some distant galaxy receding from the Earth faster then speed of light or centre of the universe?
If Big Bang theory is correct the only meaningful measurement of time, motion and distance is referencing it to the point in the universe where the Big Bang occurred, (and the time and space come to existence).

This is not right.

The theory of relativity is based on the abandonment of any absolute frame of reference for time and distance - this is the logical result of the (observed) fact that the speed of light is constant no matter where you are in the universe and no matter what your speed may be.

Kal (Andrew) · #9 21-08-2008, 03:07 PM

Carl - the simplest way to explain it is to say that no matter what speed you are travelling at, light will always appear to travel at the exact same speed to you. But some interesting changes occur. Lets say you jumped in a spaceship and started orbiting the earth at 90% the speed of light (relative to your stationary speed standing still on earth, or relative to an observer on earth). You orbit for exattly 24 hours going by your clock on your spaceship, but the people on earth observing you have actually had more time pass, for every 24 hours your clock ticks over, earth clocks tick over 55 hours! Also, to people on earth your ship would appear to be 2.29 times shorter, and 2.29 times heavier.

So as you can see, time, mass, and distance are all relative to the observer. You would look out and think your ship is 100 metres long, weighs 10 tonnes, and 1 day has passed, but people on earth would observe 2.29 days passed, a 43 metre long ship, and a ship weighing 29.2 tonnes. Which readings are true then? Well it is all relative to the observer!

MrB (Simon) · #10 21-08-2008, 03:31 PM

Quote:

but people on earth would observe 2.29 days passed, a 43 metre long ship, and a ship weighing 29.2 tonnes.

I don't even pretend to understand this stuff, but..
How does one 'observe' a ships weight?
And how do you weigh something in weightlessness anyway?
Do you mean the mass would be increased to 29.2 tonnes?
I thought mass was mass and thats that, kinda like light speed is lightspeed...
Urrrgh.... think I'll leave this stuff to those that have bigger brains than I!

Kal (Andrew) · #11 21-08-2008, 04:51 PM

Quote:

Originally Posted by MrB

I don't even pretend to understand this stuff, but..
How does one 'observe' a ships weight?
And how do you weigh something in weightlessness anyway?
Do you mean the mass would be increased to 29.2 tonnes?
I thought mass was mass and thats that, kinda like light speed is lightspeed...
Urrrgh.... think I'll leave this stuff to those that have bigger brains than I!

I won't pretent and say I completely understand it myself, I needed a relativity calculator to get those numbers, and I may have mis-interpreted them. If I'm wrong I'm sure someone will correct me though

drmorbius (Randall) · #12 21-08-2008, 08:32 PM

Good question! I love this stuff... but it makes my brain hurt...

bojan · #13 21-08-2008, 08:48 PM

Quote:

Originally Posted by MrB

I don't even pretend to understand this stuff, but..
How does one 'observe' a ships weight?
And how do you weigh something in weightlessness anyway?
Do you mean the mass would be increased to 29.2 tonnes?
I thought mass was mass and thats that, kinda like light speed is lightspeed...
Urrrgh.... think I'll leave this stuff to those that have bigger brains than I!

It is not weight but mass...
Mass increases with relative speed because the kinetic energy of moving ship has mass also (E=mc^2)
Mass can be measured.. for example, mass of the charged particles is measured in the magnetic field of known strength, where particle has curved trajectory instead of straight one. The radius of the trajectory is depending on charge, magnetic field strength and particle speed and mass.
To measure the mass of the space ship, travelling at nearly the speed of light is a bit more difficult obviously, but the same principle applies :-)

Rick Petrie · #14 21-08-2008, 11:44 PM

My thoughts or two bobs worth.
To any observer travelling at any speed, the speed of light would have to be absolute and relative to the observer.( I don't know of anyone who has seen anything travelling faster than the speed of light!)
If two spaceships could travel at the speed of light(improbable) in one direction they would therefore be able to see each other with light travelling between them at the same speed of light relative to each other. I think then in this case that ship A would see the beam of light from ship B at the speed of light between them.(Question 1 & 2)
Theoretically Question 3 would have to assume that the bullet (mass) can travel faster than the speed of light. If it could then the bullet would hit
ship A at 4500ft/sec.
Personally I don't think any matter can travel faster than the speed of light.
If that were the case then we are in deep s--t from any object in space on a collision course with Earth travelling faster than the speed of light. We definitely wouldn't have time to kiss our backsides goodbye.

Jeff · #15 22-08-2008, 12:10 AM

I appreciate the analysis below, but I have another question...

Question 4: If a female astronaut was piloting one of the space ships at close to the speed of light, would she be able to put her lipstick on? I'm concerned that when she looks in the rear view mirror to check, the image reflected will be so significantly red-shifted that her eyes will not detect any visible image, irregardless of which shade of lipstick she chooses.

PCH (Paul) · #16 22-08-2008, 02:27 PM

Quote:

Originally Posted by GTB_an_Owl

Hi Paul

i have to question your answer to Q1
if A and B are both travelling at the speed of light and A is 500 metres in front of B, the light from B will never catch A.
to my mind it will always be 500 metres behind A ?

and i would love to be in ship A - cause i could shoot B - but B could not shoot me

geoff

Agreed, - surely the light emitted from the headlight in Q1 wouldn't even move ahead of the headlight at all, as it is travelling at the speed of light already. Unless of course it's "speed of light + speed of light" if the velocities are added.

And the bullet being fired from the rear ship, - well if the velocities aren't added then it would disappear off backwards at a hell of a rate instantly and would therefore go straight thru the back of the gun and the person firing it as well. If the velocities are added, then what would happen when the bullet looses it's own velocity? Would it just 'stop' relatively speaking? Meaning in fact that it is now moving along at the speed of light since it doesn't have any 'extra' velocity left from being fired?

Just my 2c as a totally unscientific person

sjastro · #17 25-08-2008, 11:48 AM

Quote:

Originally Posted by PCH

Agreed, - surely the light emitted from the headlight in Q1 wouldn't even move ahead of the headlight at all, as it is travelling at the speed of light already. Unless of course it's "speed of light + speed of light" if the velocities are added.

And the bullet being fired from the rear ship, - well if the velocities aren't added then it would disappear off backwards at a hell of a rate instantly and would therefore go straight thru the back of the gun and the person firing it as well. If the velocities are added, then what would happen when the bullet looses it's own velocity? Would it just 'stop' relatively speaking? Meaning in fact that it is now moving along at the speed of light since it doesn't have any 'extra' velocity left from being fired?

Just my 2c as a totally unscientific person

Quote:

Originally Posted by Rick Petrie

My thoughts or two bobs worth.
To any observer travelling at any speed, the speed of light would have to be absolute and relative to the observer.( I don't know of anyone who has seen anything travelling faster than the speed of light!)
If two spaceships could travel at the speed of light(improbable) in one direction they would therefore be able to see each other with light travelling between them at the same speed of light relative to each other. I think then in this case that ship A would see the beam of light from ship B at the speed of light between them.(Question 1 & 2)
Theoretically Question 3 would have to assume that the bullet (mass) can travel faster than the speed of light. If it could then the bullet would hit
ship A at 4500ft/sec.
Personally I don't think any matter can travel faster than the speed of light.
If that were the case then we are in deep s--t from any object in space on a collision course with Earth travelling faster than the speed of light. We definitely wouldn't have time to kiss our backsides goodbye.

Neither scenario would occur. Apart from the infinite relativistic mass, ships A and B would be dimensionless in the direction of motion let alone have a 500m gap between them.

Length contraction might be a difficult concept to grasp but there is a practical application in the construction of particle accelerators. For particles with small half lives accelerated at 0.99c, the distance between the particle beam source and the target is calculated taking into account the relativistic effects.

Regards

Steven

GTB_an_Owl (Geoff) · #18 25-08-2008, 02:36 PM

and i didn't understand one word you just said Steven

you sure your not into politics rather than astronomy ?

geoff

Rick Petrie · #19 25-08-2008, 03:14 PM

Quote:

Originally Posted by sjastro

Neither scenario would occur. Apart from the infinite relativistic mass, ships A and B would be dimensionless in the direction of motion let alone have a 500m gap between them.

Length contraction might be a difficult concept to grasp but there is a practical application in the construction of particle accelerators. For particles with small half lives accelerated at 0.99c, the distance between the particle beam source and the target is calculated taking into account the relativistic effects.

Regards

Steven

I'm utterly confused at warp factor five Mr Spock.

sjastro · #20 25-08-2008, 06:09 PM

Quote:

Originally Posted by Rick Petrie

I'm utterly confused at warp factor five Mr Spock.

Quote:

Originally Posted by GTB_an_Owl

and i didn't understand one word you just said Steven

you sure your not into politics rather than astronomy ?

geoff

Well I suppose politics is the science of BS but not in this case.

Let me give an example.

Particle physicists frequently bombard atoms with unstable nuclei that have very short half lives. If the distance beween the atoms and the source of the bombarding nuclei is too great then most if not all of the nuclei would have decayed before hitting the target.

In the laboratory frame of reference the distance travelled when 50% of the nuclei decay is simply the (speed of the nuclei) X (half life measured in the laboratory).

If however the speed of the nuclei is near the speed of light (say 99%), the half life measured in the laboratory is much greater than the half life of a stationary nuclei due to time dilation. The percentage change for time dilation is the same as percentage shrinkage in distance.

Suppose the distance in the the laboratory frame between the source and the atoms is calculated to be 100 metres. (Without considering the effects of length contraction).

The corresponding distance in the nuclei's frame of reference at 99% speed of light is
100X(1-(0.99)^2)^0.5 = 14 metres.

The distance between the source and the atoms needs to be set at 14 metres for 50% of nuclei to reach their target.

As one gets closer to the speed of light the degree of contraction increases. At the speed of light contraction to zero length would occur (which of course is not possible as matter can't travel at this speed).

Hope this makes sense.

Steven