If you traveled towards a planet at 0.9C

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In summary, the stripes on a long bridge between you and the planet would get thinner as the bridge gets shorter because the time it takes for light to reach your eyes is the same no matter how long the bridge is.
  • #1
victorhugo
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Let's say there was an extremely long striped bridge between you and the planet. You get a boost towards it causing you to suddenly travel at 0.9C, would you see the horizontal stripes on the bridge get thinner as length gets contracted?

Also, the time it takes to travel the contracted length is the same as the dilated time. Does this mean dilated time is only a consequence of length contraction, which does not happen to frames of reference that are still, and thus time is distorted?
 
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  • #2
This is, of course, exactly the same as if the planet and the bridge were rushing towards you at .9c

victorhugo said:
would you see the horizontal stripes on the bridge get thinner as length gets contracted?
What you actually SEE is light reflected from the stripes and traveling through space to reach your eyes sometime later. This makes what you SEE a bit complicated because the light that hits your eyes at a given moment left different parts of the bridge at different times so the image formed on your retina is not an accurate picture of the bridge.

However, when you allow for light travel time and calculate what an accurate picture would look like... Yes, the stripes are thinner.

Also, the time it takes to travel the contracted length is the same as the dilated time. Does this mean dilated time is only a consequence of length contraction, which does not happen to frames of reference that are still, and thus time is distorted?
No, although it does mean that you can't have length contraction without time dilation (and also relativity of simultaneity - all three are needed for consistency). Neither length contraction nor time dilation are distortions that happen in moving frames but not still ones. They can't be because a frame that is at rest relative to me may be one that is moving relative to you, and vice versa - so which of us gets to say which one is distorted and which isn't? Instead, time dilation and length contraction are part of how we relate times and distances measured in one frame to times and distances measured in another frame.
 
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  • #3
victorhugo said:
Let's say there was an extremely long striped bridge between you and the planet. You get a boost towards it causing you to suddenly travel at 0.9C, would you see the horizontal stripes on the bridge get thinner as length gets contracted?

Also, the time it takes to travel the contracted length is the same as the dilated time. Does this mean dilated time is only a consequence of length contraction, which does not happen to frames of reference that are still, and thus time is distorted?
I made some videos here of relativistic flight (including a striped floor). Note that they are not constant-velocity flights, they are accelerated, but this means that you can see how the effects change with velocity.

Please read the notes on the page if you want to know the grubby details. They are terse, but should give you some search terms to look up if you want more background.
 
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  • #4
m4r35n357 said:
I made some videos here of relativistic flight (including a striped floor). Note that they are not constant-velocity flights, they are accelerated, but this means that you can see how the effects change with velocity.

Please read the notes on the page if you want to know the grubby details. They are terse, but should give you some search terms to look up if you want more background.
I don't see the one probably of most interest to the OP: looking directly down at a relativistically moving striped floor (stripes orthogonal to direction of motion). This would visually show length contraction.
 
  • #5
PAllen said:
I don't see the one probably of most interest to the OP: looking directly down at a relativistically moving striped floor (stripes orthogonal to direction of motion). This would visually show length contraction.
ON re-reading the OP I still think he is talking about the stripes as I have them. Perhaps victorhugo would care to clarify. BTW this is stuff I already had, I did not make it for the OP ;)
I know we are talking about relativity, but I find it odd that the OP is talking about being on a moving ship, whereas you are talking about a moving floor. Are you sure you read it right? I know what I mean by "horizontal stripes" in this context.
Hmm, on re-reading your comment, you are talking about the same kind of stripes as I am. There are three videos with such stripes; a non-relativistic one, one with a = moon gravity and one with a = Earth gravity.
There are also side views. I am now totally puzzled, but it's time for bed now.
 
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  • #6
m4r35n357 said:
ON re-reading the OP I still think he is talking about the stripes as I have them. Perhaps victorhugo would care to clarify. BTW this is stuff I already had, I did not make it for the OP ;)
I know we are talking about relativity, but I find it odd that the OP is talking about being on a moving ship, whereas you are talking about a moving floor. Are you sure you read it right? I know what I mean by "horizontal stripes" in this context.
Hmm, on re-reading your comment, you are talking about the same kind of stripes as I am. There are three videos with such stripes; a non-relativistic one, one with a = moon gravity and one with a = Earth gravity.
There are also side views. I am now totally puzzled, but it's time for bed now.


The OP is not talking about gravity at all. The OP described flying over a striped bridge, and my guess is they meant looking directly down at it. Nugatory pointed out the this scenario can identically be described as the striped bridge moving under you. I consider these the same scenario, as there is only one invariant answer to what you would see. It seems to me you are drastically overcomplicating what the OP is asking.
 
  • #7
I am showing what a striped floor looks like at relativistic speeds, as explicitly mentioned by th OP. The "gravity" you object to is just g-force. I don't see what you are upset about.
 
  • #8
I suggest that we wait and see if OP returns, let's us know what he understands so far.
 
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  • #9
m4r35n357 said:
I am showing what a striped floor looks like at relativistic speeds, as explicitly mentioned by th OP. The "gravity" you object to is just g-force. I don't see what you are upset about.
Ok, but you show it looking forward, not straight down. The approach adds more complex visual distortions.
 
  • #10
Looking in the direction of motion you see what is below you owing to aberration. Looking down would show what is behind you. An accelerated view shows all these things. The "moon gravity" video gives a less distorted view.
 
  • #11
m4r35n357 said:
I made some videos here of relativistic flight (including a striped floor)...
Very good video (and channel, too. I've suscribed it) But no "like" collected. I'm the first I guess :smile:
 
  • #12
Stephanus said:
Very good video (and channel, too. I've suscribed it) But no "like" collected. I'm the first I guess :smile:
Thanks. You can probably guess that I didn't do it for the likes; I did it to learn, and I learned more than I expected doing it. I can thoroughly recommend computing stuff (in addition to pen & paper, computer algebra etc.) wherever feasible to get a feel for the equations. Those videos actually started out as a spreadsheet, then I saw the weird shapes on the plots, and imagined rays from the eye to each point. This is where POVRay came in, and it has a rudimentary animation feature. That's how things can snowball!

Shame the OP never returned though . . .
 
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  • #13
m4r35n357 said:
ON re-reading the OP I still think he is talking about the stripes as I have them. Perhaps victorhugo would care to clarify. BTW this is stuff I already had, I did not make it for the OP ;)
I know we are talking about relativity, but I find it odd that the OP is talking about being on a moving ship, whereas you are talking about a moving floor. Are you sure you read it right? I know what I mean by "horizontal stripes" in this context.
Hmm, on re-reading your comment, you are talking about the same kind of stripes as I am. There are three videos with such stripes; a non-relativistic one, one with a = moon gravity and one with a = Earth gravity.
There are also side views. I am now totally puzzled, but it's time for bed now.
Thanks. It would be fantastic if you could you please put some descriptions in your videos. Not just the math, but also a detailed description of what we are looking at.
 
  • #14
Did you read the notes on the page itself that I mentioned in post #3 (the "more" link)? That is all I've had time to do, and hopefully there are enough clues there for you to at least ask a more specific question as and when you need (there is a lot going on as I said before). I can't expand the whole lot in one go! There is also a GitHub project with all the files in it here, if you are reasonably confident with using POV-Ray, FFmpeg, shell etc.
 
  • #15
m4r35n357 said:
Thanks. You can probably guess that I didn't do it for the likes; I did it to learn, and I learned more than I expected doing it. I can thoroughly recommend computing stuff (in addition to pen & paper, computer algebra etc.) wherever feasible to get a feel for the equations. Those videos actually started out as a spreadsheet, then I saw the weird shapes on the plots, and imagined rays from the eye to each point. This is where POVRay came in, and it has a rudimentary animation feature. That's how things can snowball!

Shame the OP never returned though . . .
Of course you don't. But still I like it :smile:
 
  • #16
Nugatory said:
They can't be because a frame that is at rest relative to me may be one that is moving relative to you, and vice versa - so which of us gets to say which one is distorted and which isn't? Instead, time dilation and length contraction are part of how we relate times and distances measured in one frame to times and distances measured in another frame.

Does this mean that both of the frames that are moving relative to each other will have the same time dilation and length contraction measured in the other frame?
 
  • #17
Shafia Zahin said:
Does this mean that both of the frames that are moving relative to each other will have the same time dilation and length contraction measured in the other frame?
Yes. You also need to consider the relativity of simultaneity in order for this to make complete sense.
 
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  • #18
*returns 6 months later*

Thank you for all the answers, they all addressed my question correctly.
However, what I mean in
"Also, the time it takes to travel the contracted length is the same as the dilated time. Does this mean dilated time is only a consequence of length contraction, which does not happen to frames of reference that are still, and thus time is distorted?"

Is this:
(assuming c = 3x10^8)
travelling at 0.9C through a distance of 1x10^9m it would take me t = 3.704... seconds, as seen from the frame of reference at the end/beginning of that distance.

however, at 0.9C I'd see the length to be: d x [(root)1-(0.9^2)] = 4.359 x10^8 metres

From this length contraction, the time to reach the end of the distance as seen from my frame is then t = d/s = 1.614 s
Considering the time observed from the outside frame, we can calculate my time to be
3.704 x root 1-.9^2 = 1.615 s

so my conclusion is that time dilation occurs as a result of length contraction.
 
  • #19
victorhugo said:
so my conclusion is that time dilation occurs as a result of length contraction.
You can't have one without the other, so it's pretty much arbitrary which one causes the other. Consider a flash of light is emitted at one event and detected at another event. If the speed of light is going to be ##c## no matter which frame you use to assign coordinates to these events, then the equation ##T=L/c## must hold no matter which frame you use to calculate ##L## and ##T##; if different frames yield different values for one of those quantities they must also yield different values for the other.

It's better to think of length contraction and time dilation as two sides of the same coin, and that both are "caused" by relativity of simultaneity. We have many threads here explaining how you cannot define the rate at which one clocks tick compared with another (time dilation) or the length of one measuring stick compared with another, without using the notion of "at the same time". When "at the same time" changes according to the frame you use, time dilation and length contraction must necessarily appear.
 

1. What is the speed of light and why is it important in this scenario?

The speed of light is approximately 299,792,458 meters per second. It is important in this scenario because it is the universal speed limit in the universe, meaning that nothing can travel faster than the speed of light. This includes objects such as planets and spacecraft.

2. How long would it take to reach the planet at 0.9C?

Assuming the planet is 10 light years away, it would take approximately 11.1 years to reach the planet at 0.9C. This is because time would dilate for the traveler due to the effects of special relativity. However, for an outside observer, the journey would appear to take much longer, around 111 years.

3. What would happen to the mass of the spacecraft as it approaches the speed of light?

As the spacecraft approaches the speed of light, its mass would increase significantly due to the effects of special relativity. This is known as relativistic mass, and it would cause the spacecraft to require more energy to continue accelerating. However, the increase in mass would not be noticeable to the naked eye.

4. Would time pass differently for the traveler compared to someone on Earth?

Yes, time would pass differently for the traveler due to time dilation. As the spacecraft approaches the speed of light, time would slow down for the traveler. This means that when they return to Earth, they would have experienced less time than those on Earth. This has been proven through experiments with atomic clocks on spacecraft.

5. What other factors would need to be considered when traveling at such a high speed?

Other factors to consider would be the effects of special relativity on the traveler's perception of time and space, the potential increase in mass of the spacecraft, and the immense amount of energy required to reach speeds close to the speed of light. Additionally, the potential dangers of traveling through space, such as collisions with debris or radiation exposure, would also need to be carefully considered and planned for.

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