If you traveled towards a planet at 0.9C

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Main Question or Discussion Point

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?
 

Answers and Replies

  • #2
Nugatory
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This is, of course, exactly the same as if the planet and the bridge were rushing towards you at .9c

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 travelling 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.
 
  • #3
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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?
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.
 
  • #4
PAllen
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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
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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
PAllen
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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
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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
Nugatory
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I suggest that we wait and see if OP returns, let's us know what he understands so far.
 
  • #9
PAllen
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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
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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
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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
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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 . . .
 
  • #13
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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
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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
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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
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
Ibix
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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.
 
  • #18
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*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
Nugatory
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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.
 

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