Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: m harnack on 19/07/2019 16:34:20

Understanding Special Relativity for Amateurs
This scenario has been written to assist in the understanding a multitude of aspects of special relatively for the amateurs of us interested in cool physics (including me). I would be grateful for a physicist with a University degree to answer in detail (sorry no half baked musings on this on please).
Scenario:
C < 100 million light years > A < 100 million light years > B
1 > (a = 20 m/s/s until 0.99999c)
2 > (a = 20 m/s/s until 0.5c)
< 3 (a = 20 m/s/s until 0.99999c)
< 4 (a = 20 m/s/s until 0.5c)
Primary Details:
 Spaceships 1 and 2 set out from observer A towards observer B who is 100 million light years away. Each accelerate at 20 m/s/s (i.e. ~2g) until cruising velocity is made. 1 accelerates to 0.99999c while 2 only accelerates to 0.5c
Similarly spaceships 3 and 4 set out from observer A to C.
 Each spaceship also decelerates at 20m/s/s as it approaches the target observer such that they stop when they reach the target.
 1, 2, 3, 4, A, B, C are all fitted with 6 lasers each, directed to each of the different observers and spaceships. The lasers flash once per 100 seconds for 1 second duration. i.e. on the 99th second the lasers turns on for 1 second. The light is green (wavelength of say 532 nm).
Secondary Details for Auxiliary questions :
 Each laser makes 1 GW of effective light emitted during the 1 second bursts.
 Each spaceship weighs 10 Tonnes excluding fuel. Let's assume each ship has some sort of particle accelerate to use as thrust that can accelerate the particles used as thrust to ~0.9c. Also it is powered by let's say some theoretical antimatter/matter source and the whole system can convert all matter into thrust at 99.9% energy efficiency.
Assumptions:
 Each observer is stationary relative to the others (i.e. in the same velocity frame) and also in a straight line such that observers C and B are 200 million light years away from each other.
 Please ignore the expansion of the universe.
 200 million years ago (according to A), observer A sent a message to observers B and C that this experiment would commence at the specific time. So 100 million years prior to launch A, B, C started their lasers flashing. Everyone is prepared for their observations (when the light from each item finally reaches each observer) and have started their local timers at the same time.
Q1.
a) According to spaceship 1, how long did it take to reach B?
b) According to spaceship 1, when does spaceship 2 arrive at B?
c) describe, inducing a rough timeline, what spaceship 1 observes from the laser lights (i.e. the wavelength, how long between flashes and duration of flashes, the energy intensity) , originating from A, B, 2, 3, 4 as it accelerates to 0.99999c, cruises at 0.99999c, and finally approaches B.
Q2.
a) According to spaceship 2, how long did it take to reach B?
b) According to spaceship 2, when does 1 arrive at B?
c) describe, including a rough timeline, what spaceship 2 observes from the laser light originating from A, B, 1, 3, 4 as it accelerates to 0.5c, cruises at 0.5c, and finally approaches B.
Q3.
a) According to observer B, when does 1 reach it?
b) According to observer B, when does 2 reach it?
c) Describe, including a rough timeline, what observer B observes from the laser light originating from 1, 2, 3, 4.
Q4.
a) According to observer A, when does 1 reach B?
b) According to observer A, when does 2 reach B?
c) Describe, including a rough timeline, what observer A observes from the laser light originating from 1, 2, 3, 4.
d) According to observer A, how fast are 1 and 3 moving away from each other?
Auxiliary Questions.
a) how much fuel do spaceship 1 and 2 need.
b) If each laser had a narrow enough focus and the observers had a large enough receiver to capture all of the light emitted to them from each spaceship, what would the energy levels (GW) look like from each spaceship.

Please phrase your title as a question as requested in the forum usage policy.
Thank you
By the way, is this a homework question?
PS you don’t get to be a physicist nowadays without having at least a university degree.

You need to change your topic title per the first reply, and also because the OP has a lot of questions, none of which are the 'ultimate' one.
This scenario has been written to assist in the understanding a multitude of aspects of special relatively for the amateurs of us interested in cool physics (including me). I would be grateful for a physicist with a University degree to answer in detail (sorry no half baked musings on this on please).
While my answers are not half baked musings, I doubt there are any actual relevant physicists on forums like this one. You want an educated answer, fine, but it's not going to come from a physicist.
Scenario:
C < 100 million light years > A < 100 million light years > B
1 > (a = 20 m/s/s until 0.99999c)
2 > (a = 20 m/s/s until 0.5c)
< 3 (a = 20 m/s/s until 0.99999c)
< 4 (a = 20 m/s/s until 0.5c)
Primary Details:
 Spaceships 1 and 2 set out from observer A towards observer B who is 100 million light years away. Each accelerate at 20 m/s/s (i.e. ~2g) until cruising velocity is made. 1 accelerates to 0.99999c while 2 only accelerates to 0.5c
Similarly spaceships 3 and 4 set out from observer A to C.
It isn't really stated, but I presume from this description that C, A, and B are locations in some reference frame and that the observers so named are stationary at those locations and the distance given (the 100m LY) is measured in that frame.
The fact that you have accelerating ships kind of gets into accelerated reference frames which is covered better under general relativity (GR), but special relativity also covers it. It just requires more calculus than would something like instant acceleration scenarios.
The pairs of ships accelerate side by side until the slow ones quit and the faster ones continue to accelerate up to the higher speed.
 Each spaceship also decelerates at 20m/s/s as it approaches the target observer such that they stop when they reach the target.
 1, 2, 3, 4, A, B, C are all fitted with 6 lasers each, directed to each of the different observers and spaceships. The lasers flash once per 100 seconds for 1 second duration. i.e. on the 99th second the lasers turns on for 1 second. The light is green (wavelength of say 532 nm).
Secondary Details for Auxiliary questions :
 Each laser makes 1 GW of effective light emitted during the 1 second bursts.
 Each spaceship weighs 10 Tonnes excluding fuel. Let's assume each ship has some sort of particle accelerate to use as thrust that can accelerate the particles used as thrust to ~0.9c. Also it is powered by let's say some theoretical antimatter/matter source and the whole system can convert all matter into thrust at 99.9% energy efficiency.
If it exhausts the reaction mass at 0.9c, it is 90% efficient by that metric. It really doesn't make a different if it is antimatter drive or water rocket like the space shuttle.
Please ignore the expansion of the universe.
It wouldn't be SR if we assumed otherwise.
Q1.a) According to spaceship 1, how long did it take to reach B?
~447222 years
b) According to spaceship 1, when does spaceship 2 arrive at B?
When the ships rejoin, the clock on ship A reads about 100446222 years.
c) describe, inducing a rough timeline, what spaceship 1 observes from the laser lights (i.e. the wavelength, how long between flashes and duration of flashes, the energy intensity) , originating from A, B, 2, 3, 4 as it accelerates to 0.99999c, cruises at 0.99999c, and finally approaches B.
The flashes are all the same at first.
Once everything is up to cruising speed, the light from A is dilated by a factor of about 223.6 and a Doppler factor of 100k, so it blinks around 22.36 million times slower. Light from B is dilated by 223.6 again, but Doppler is in the other direction, so it blinks 447 times faster. Frequency shifts are also proportional.
To do one more, the fast ship 3 has a gamma of about 1e5 and a Doppler factor of about 1e10 so it blinks about 1e15 slower.
a) According to spaceship 2, how long did it take to reach B?
I get 173 some million years
b) According to spaceship 2, when does 1 arrive at B?
Frame dependent question since spaceship 2 is not present at that event.
describe, including a rough timeline, what spaceship 2 observes from the laser light originating from A, B, 1, 3, 4 as it accelerates to 0.5c, cruises at 0.5c, and finally approaches B.
At cruise, gamma is 1.1547 and Doppler is a factor of two, at least relative to the lettered objects. It can be worked out from that.
Ship 1 is moving at .99987c so those two ships see blinking slowed from each other by about 6.2 million
]a) According to observer B, when does 1 reach it?
b) According to observer B, when does 2 reach it?
We haven't stated what the clock at B reads at any particular event, so this cannot be known. If it is synced to A in that original frame, then ship 1 gets there at year 100001000 and ship 2 at 200MYr (plus about 100 days). This is pretty trivial arithmetic.
c) Describe, including a rough timeline, what observer B observes from the laser light originating from 1, 2, 3, 4.
Same thing that those ships saw when observing B.
As for timeline, B will observe nothing for 100m years since the departure event takes that long to be seen. So ship 1 appears to be in flight only the last 1000 years, and ship 2 for the 2nd half of the duration. All 4 ships appear to get up to cruising speed relatively quickly. 20 m/sec² will definitely get you there.
a) According to observer A, when does 1 reach B?
b) According to observer A, when does 2 reach B?
Assuming the frame of A and that clocks are synced in that frame, all these events are the same answer as B's answer.
c) Describe, including a rough timeline, what observer A observes from the laser light originating from 1, 2, 3, 4.
Same as those that seen by the ships looking at A.
d) According to observer A, how fast are 1 and 3 moving away from each other?
That's a 3 way relation, not particularly defined. Ships 1 and 3 are moving at .99999999995c relative to each other period. It's an objective relation, not a frame dependent one.
b) If each laser had a narrow enough focus and the observers had a large enough receiver to capture all of the light emitted to them from each spaceship, what would the energy levels (GW) look like from each spaceship.
Work it out as a function of energy conservation.

Hmm, if that was the simple one I fear for the complex.

Hmm, if that was the simple one I fear for the complex.
You are obviously a half wit, as an amateur i find this explains everything concisely.

Hmm, didn't mean to anger you, just that there are simpler approaches..
But that may just be how I look at it.
Everyone's different

Hmm, didn't mean to anger you, just that there are simpler approaches..
But that may just be how I look at it.
Everyone's different
no, it was sarcasm, i agree with you that its not exactly strait forward

Hmm, if that was the simple one I fear for the complex.
You are obviously a half wit, as an amateur i find this explains everything concisely.
Why even say that in the first place? There are an unending number of ways to express "i agree with you that its not exactly strait forward" without resorting to your choice of words.
Did calling someone a halfwit seem absolutely necessary? Where was the apology? I didn't read it. Maybe you should think before you type

Hmm, if that was the simple one I fear for the complex.
You are obviously a half wit, as an amateur i find this explains everything concisely.
Why even say that in the first place? There are an unending number of ways to express "i agree with you that its not exactly strait forward" without resorting to your choice of words.
Did calling someone a halfwit seem absolutely necessary? Where was the apology? I didn't read it. Maybe you should think before you type
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