Relativity Question ? Can it be explained ?

Ok. I know there's been 1,000's of these. Please bear with me.

A spaceship 1/2 lightyear long, travelling close to the speed of light, has just reached a spot 1/2 light year away from Earth. An, extremely bright light, is switched on at the far end of the spaceship ( 1 l/y from Earth ) on both the inside & the outside of the ship.

The light will reach the front of the spaceship (inside) in 1/2 year, as their local light travels at the speed of light in their time frame. This would be just as the front of the spaceship reaches Earth ? The outside light source wont reach Earth for another 6 months !!

If you open a door at the front of the spaceship as it reaches Earth, the light inside the ship has reached Earth and would be visible to an observer on Earth, twice as fast as the light outside of the spaceship.

Both light sources are in the same timeframe as far as an observer on Earth is concerned. Both light sources should be travelling at the speed of light compared with the occupants of the ship, so does the light reach Earth in a year or 6 months !!

I don't believe that any of the relativity arguments posted so far explain this one ? In fact this looks like a good logical argument to disprove the theory ? But if I'm wrong, I'm sure someone will point it out.

Please, no formulas or dodgy quotes from other people. No, "someone who's an expert says it's so, so it's so". Just some logical arguments why this aint so !!

Come on. Explain it. Can't be done can it ?

No. Light in the aircraft can't travel at just the speed in the local time frame. No the light can't travel in time because it's in a spaceship travelling close to the speed of light. No, it doesn't make a difference to an observer on Earth whether the light is inside or outside of the spaceship. No, it makes no difference to the passengers inside the craft whether the light is inside or outside the ship.


So where's the error ?? It don't work !!! Maybe we should just ignore it like all of the other bits that don't add up ? Ignore it. Invent another dimension to hide the problem in ?? A new constant won't work !!


Yes. I know some bright spark is going to come up with a proof to make me feel silly. But, hey, I'm never goin to meet any of you so what do I care and at least I'll learn something .... maybe.

Come on ....

 

Log in or Sign up to hide all adverts.

Quite simple - light will travel at c regardless of the sources of light and the observers.

 

Log in or Sign up to hide all adverts.

Log in or Sign up to hide all adverts.

Hmmm... something's wrong here...
I think that at the time the light is emitted, the distance from the rear of the ship to Earth as measured on the ship will be:
d = (1ly)/(10000) = 0.0001ly (about 10⁹km)

Ship time for light to reach Earth = 52 minutes 35.76 seconds
Ship time for rear of ship to reach Earth = 52 minutes 35.7600016 seconds

As you can see, Mike, this isn't an easy subject for explanations!


The simple explanation is that a constant speed of light implies some other weird and wonderful things that are extremely counter-intuitive, and thus very difficult to accept.

For observers moving relative to each other:
Time delays between events will be different (time dilation)
Distance between events will be different (length contraction)
Space is not constant - "The same place" means different things to each observer
Time is not constant - "At the same time" means different things to each observer

The observers agree on "events" - things that happen at a given place and time, but:
If two events happen at the same time and different places for one observer, they will probably happen at different times for the other observer.
If two events happen at the same place and different times for one observer, they will happen at different places for the other observer.

It's wonderfully head-spinning stuff until you understand it... then it's just maths (but still lots of fun to think about).

 

Okay. That hurt.

I've only come across time being affected by differences in velocity. Are you saying that the dimension of objects is also affected ? ie. the 1/2 ly length ship is close to zero l/y in length ?

Whether or not the ship is measured as 1/2 ly in length from Earth, it presumably is actually 1/2 ly in length ?

If we're saying that you can adjust the dimensions & time to fit into the rules of relativity, isn't this a 'Get Out of Jail Free' card that you can use for any argument that suggests that the theory is wrong ?

Can you confirm whether, as far as the theory goes, the ship itself is actually near a zero length to an observer on Earth or just observed as zero length ?

 

Not dimensions only one dimension. That of length in the direction travelled.

Apparently, it IS zero length to an observer on earth. Length, like time is not a constant property of something. "It is all relative !"

 

That does explain the proposed problem.

Okay, you asked for it ...

The ship is 1m long (ie. nearly zero) & 1/2 ly wide. The front is 1/2 ly from Earth & it's travelling at nearly c. A laser on the left (wherever that is) side is switched on (inside&outside) directed across the ship and is reflected by a 45 degree mirror on the right side and also a fixed mirror positioned just outside the right hand window (fixed at the starting point). The inside mirror redirects the laser out of the front window.

When the ship reaches earth 1/2 year later the light source inside the ship is just appearing out of the front window, having taken 1/2 year to travel across the ship, but the light reflected by the fixed external mirror will take another 6 months to turn up ?

Now, if only the 'approaching' dimension is affected, the original argument still holds. Unless ALL dimensions are compressed ??

In addition, for someone on Earth, the light source inside the ship has travelled diagonally across a square, 1/2 ly by 1/2 ly, in only 1/2 year, which means it's travelled faster than c ??

 

For the inside ship observer all is normal. The light is traveling the entire length of the ship at c inside and outside because the beams are moving relative to the ship. The light appears as a diagonal to the outside observer but it doesn't travel faster than c. Think about it this way. You are looking at the ship itself in all its half lightyear glory in the same way you are looking at the beam. The ship will appear to be "bent" as a diagonal itself so to speak to the outside observer (but I guess it depends on where you are observing it from). At least I think that is what happens....can someone backup or correct the statement above?

 

Yep - in Earth's frame of reference, it's close to zero long.

The proper length is 1/2 ly - the "proper length" of the object is its length in its own reference frame.
In Earth's reference frame, it actually is close to zero long.

Interesting question!
The idea that the speed of light is invariant came first, primarily from Maxwell's work in electromagnetics. It was generally thought that this implied an aether, which would provide a universal reference frame.
However, experiments that attempted to detect the aether (the Michelson-Morley experiment is the most well known) were fruitless.

To resolve the issue, Einstein proposed the Principle of Relativity:

The description of all phenomena provided by any two observers in uniform relative motion are equally valid; the laws of physics are the same for both of them.​

This is actually a generalisation of Galilean relativity, which suggested that the laws of mechanics are the same for all observers.

In particular, this implied the absoluteness of the speed of light in a vacuum: it is the same for any two observers in uniform motion.

Einstein then explored the idea - if the speed of light is invariant for all observers, what other implications are there?

That is where the adjustment of time and length and other wonderful things in relativity come from - they are direct implications of lightspeed invariance:

Moving clocks run slow
Moving rulers are shorter (in the direction of travel)
Simultaneous events are not simultaneous for moving observers
Moving masses have greater inertia​

So rather than "fudge factors", these effects are tests of relativity. If the speed of light is really invariant, then the effects must be true.

Therefore, if the effects are found to not occur, then relativity must be flawed.

You can find more info in lots of places online and off.
Here's one that looks OK: Syracuse University

 

Is the ship 1/2 ly from Earth in the ship's frame, or in Earth's frame?

I'm not following the setup of your lasers and mirrors.
The lasers (in and out) are on the left-hand end, pointing right?
Is there a mirror at each end, or are they both on the right?
When the ship reaches Earth, where is Earth with respect to the ship? Left end, right end, or middle?

 

Apoligies. Not enough detail given.

Ship is 1/2 ly from Earth in Earth's timeframe. ( Are the distances different ? I guess so, as all distances in that direction are compressed ? ). Travelling at close to c in Earth's timeframe (not sure if this is relevant ? ).

Effectively, the laser sends light from the far left of the ship to the far right & is directed out of the front window by a 45 degree mirror. The outside laser does the same but on the outside of the ship using a fixed mirror.

When the ship reaches Earth, the viewer is looking directly through the right hand window. The light from the fixed mirror would also reach the exact point where the viewer is standing.

Is this enough ?

 

Oooh - that's a tricky one.
I don't think I have the expertise to do it, because I'm a bit fuzzy on relative simultaneity...

Can anyone help out an armchair physicist?

 

After thinking about this, I realise that it has nothing to do with relative simultaneity at all.
Let's use a relative speed of 99.5% light speed, which gives a nice round Lorentz factor of 10.

To make it easier for me, I'm going to make the ship only one light-second long (300,000km), and have the laser fire when it is one light-second away from Earth (in Earth's frame).

Laser fires at left hand end of ship at t=0.

When does the laser beam reaches the right hand end of the ship?
In the ship's frame, it get's there one second later.
But in Earth's frame, the ship time is dilated by a factor of ten. The beam reaches the right hand end of the ship ten seconds later in Earth's frame.
By that time, the ship has travelled 9.95 light seconds in Earth's frame, which is 8.95 light-seconds beyond Earth (we'll use this number as a reality check later).
So in Earth's frame, the beam has travelled a long way - across the hypotenuse of the triangle formed by the ship length and travel distance. The beam has travelled √(1² + 9.95²) = 10 light-seconds.

Reality check:
Since the beam must travel at light-speed in Earth's frame as well as the ship's frame, it is good that it went 10 light-seconds in 10 seconds!

In the ship's frame, Earth is approaching at 99.5% light speed, and is only 0.1 light-seconds away when the laser fires at t=0. The beam reaches the right-hand end of the ship one second later, when Earth is 0.895 light seconds in the other direction.

Reality check:
Let's say there is a space station stationary with respect to Earth that is placed just right to catch the laser beam when it reaches the right-hand end.
In the ship's frame, it is 0.895 light-seconds past Earth.
So by time dilation it must be 8.95 light-seconds away in Earth's frame.
This is good - it matches our previously determined distance that the ship travels beyond Earth during the laser-beam's journey in Earth's frame.

Some diagrams may help.
The Earth's Frame diagram is reduced by a factor of ten.
Note how the length contraction in the Ship's Frame flattens Earth.

Earth's Frame
<img src="/attachment.php?attachmentid=2866&stc=1">

Ship's Frame
<img src="/attachment.php?attachmentid=2867&stc=1">​

 

Okay. Close but a hidden glitch ?

In both the ship's and the Earth's timeframe, the ship is 1 ly wide. So this would mean that the light travelled at c outside the ship and c/10 inside the ship, relative to the Earth ??

Or relative to the ship, the light inside the ship travelled at c and the light outside travelled at 10c ??

Also, I was under the impression that space/time was only dilated in the direction of the difference in velocity, ie. in the direction between the spaceship and the Earth, not at right angles to that direction ? The only space / time dilation should be in the distance to Earth, not in any other direction ?

So the question still stands ?????

 

Hi Mike,
Yes - from the observer's point of view, the light is travelling at c/10 relative to the ship. This is not a glitch!

Length contraction and relative simultaneity is dependant on the direction of travel, but not time dilation.


You might be interested in some further reading here: Usenet Relativity FAQ, in particular this page. I'm happy to keep discussing it here too, of course.

It's good that you're analysing my responses carefully, by the way.
This is quite a stimulating conversation!

 

Hold on. Light can't be travelling at c/10 relative to anything ? It has to be c in all timeframes ?

If time dilation affects ALL dimensions, then the light will reach the far right of the ship in 1/10 yr (in Earth's timeframe) instead of 1 yr and will be 9/10 yr ahead of the light outside the ship. This would mean that the two beams of light travelled at different speeds relative to the observer on Earth ??

In fact, if time dilation affects ALL dimensions but space dilation doesn't, in the ship's space/time frame, the light would take 10 years to reach the far end of the ship, which is only 1ly wide ??

Either way, from the perspective of an observer on Earth, the beam of light inside the ship would reach Earth across a square 1ly X 1ly in 1yr and have travelled faster than c relative to an observer on Earth. It wouldn't matter that the beam of light were inside the ship, it should still travel at c relative to Earth ?

 

No, because time dilation of the space ship is only measured by the Earth frame of reference not by the space ship frame. From the space ship frame, the light takes 1 year to cross the ship (At c).

From the Earth frame, the light travels the diagonal, and takes 10 years to cross the ship (at c). But, since the Earth frame also measures a time dilation for the spaceship, the Earth frame sees that time runs at 1/10 speed on the ship.
Thus all time measuring devices on the ship run 1/10 as fast and in ten years Earth time will only show 1 yr as passing. Thus the light reaches the opposite side of the ship when the ship's clock reads 1 yr according to Earth as well as according to the ship.

Of course this means that according to the Earth frame, the light travels at 1/10c relative to the ship, but this is not a problem, as Relativity does not forbid this. It only says that light must travel at c relative to any frame from which the measurement is being made.

 

Yes, that's right.
Relative to the ship, the beam is travelling at c.
Relative to the Earth, the beam is travelling at c.
From Earth's point of view, it appears that the beam is travelling at c/10 relative to the ship, but that it not forbidden by relativity. The speed of light postulate only dictates that a beam of light always travels at c relative to an observer as viewed by that observer.

No.
In the ship's frame, the beam takes 1 yr to travel 1 lt yr (end to end).
In Earth's, the time between these two events in the ship's frame (start and end of travel) is dilated by a factor of ten, So the beam takes 10 yrs to travel from start to end. Since the start and end are 10 lt yrs away (1 lt yr across, 9.95 lt yrs long), the beam is obviously travelling at c.

 

Okay. Now I'm lost. I think it's the numbers. Let's summarise, the 'rules' ...

- The ship is 1ly wide in both Earth's and the Ship's timeframe. (distance is not dilated in ALL dimensions).
- The ship is 1ly away in Earth's timeframe but only 1/10 ly away in the Ship's timeframe. (distance is dilated in the direction of the difference in velocity)
- Time is dilated in all dimensions, but distance only in the direction of the difference in velocity.
- c is constant in ALL timeframes.
- Light on the ship will travel at c relative to an observer on the Ship or on Earth.
- Light outside of the ship will travel at c relative to an observer on the Ship or on Earth.

Are these all correct or have I missed something ??

 

OK

OK

While I know what you are trying to say here, it doesn't really make much sense to talk about time in that way. Time automatically encompasses all the spatial dimensions. There is just one time dimension. There is not a separate time dimension for each spatial dimension.
Other than that, OK

OK

OK, as long as it is measured by that observer.

OK, same stipulation as above.