Does SR Length Contraction Halve Space Travel Time?

[Chenkel]

Hello everyone,

I've been learning about length contraction and started to ponder how it applies to space travel.

If the Lorentz factor is 2 by traveling at .577c does that mean you would be able to get to the object in half the distance because the transformed length in your reference frame is the proper distance divided by 2?

Thanks in advance.

 

[Ibix]

If the Lorentz factor is 2 by traveling at .577c

0.866c, I hope.

does that mean you would be able to get to the object in half the distance because the transformed length in your reference frame is the proper distance divided by 2?

Remember that in a frame where the distance is length contracted it is because the rocket is stationary and the stars are moving. So you don't go to the stars in this frame - they come to you. It's important to keep these things straight in your head to avoid confusion about which frame you're thinking about.

But yes, the shortened distance is your explanation for why you don't age as much as a naive Newtonian calculation would suggest. We say you were time dilated and aged slowly; you say your clocks were normal and the distance was shortened.

This is normaly illustrated with the example of cosmic ray muons.

 

[Chenkel]

0.866c, I hope.

Remember that in a frame where the distance is length contracted it is because the rocket is stationary and the stars are moving. So you don't go to the stars in this frame - they come to you. It's important to keep these things straight in your head to avoid confusion about which frame you're thinking about.

But yes, the shortened distance is your explanation for why you don't age as much as a naive Newtonian calculation would suggest. We say you were time dilated and aged slowly; you say your clocks were normal and the distance was shortened.

This is normaly illustrated with the example of cosmic ray muons.

Couldn't either the spaceship or the destination be chosen as a rest frame? I chose the spaceship as the rest frame for the calculation with the stars and destination "moving" towards the spaceship (keep in mind I imagine the relative velocity is achieved by the spaceship in the thought experiment)

Also sorry if I miscalculated the Lorentz factor, I was using AI to speed up my calc.

 

[Chenkel]

0.866c, I hope.

Remember that in a frame where the distance is length contracted it is because the rocket is stationary and the stars are moving. So you don't go to the stars in this frame - they come to you. It's important to keep these things straight in your head to avoid confusion about which frame you're thinking about.

But yes, the shortened distance is your explanation for why you don't age as much as a naive Newtonian calculation would suggest. We say you were time dilated and aged slowly; you say your clocks were normal and the distance was shortened.

This is normaly illustrated with the example of cosmic ray muons.

Got my AI saying v = .866c like you said to get a Lorentz factor of 2.

Thanks for pointing that out.

 

[PeterDonis]

Couldn't either the spaceship or the destination be chosen as a rest frame?

Of course you can--but whichever frame you choose, you have to reason consistently based on that frame. If you choose the spaceship's frame, you can't say the spaceship is moving and you can't reason about what happens based on the spaceship moving, being length contracted, time dilated, etc., because in that frame it isn't moving, it isn't length contracted, and it isn't time dilated.

 

[Vanadium 50]

0.866c, I hope.

But officer....I was only going 0.577c!

Got my AI saying v = .866c l

Do not trust them. They are not reliable.

I would suggest you working through a few chapters of a text, like Taylor and Wheeler. While nothing said so far as wrong, often people get multiple applications of the time-dilation and length-contraction formulas wrong, and it is better to get these straight from the beginning.

 

[Nugatory]

Couldn't either the spaceship or the destination be chosen as a rest frame?

Yes. Using either frame you will find that traveler, moving relative to earth and destination, finds that they reach the destination in less time than a naive non-relativistic calculation suggests. The frame in which the traveler is at rest explains this by saying that the distance is length-contracted so it takes less time on the normally ticking clock to make the journey; the frame in which the ship is moving explains this by saying that the ship's time is dilated so less time passes on the ship as it covers the uncontracted distance.

Note that to reconcile these explanations you will also have to consider the relativity of simultaneity. The explanation using the earth-at-rest frame includes an unstated assumption about simultaneity.

Got my AI saying v = .866c like you said to get a Lorentz factor of 2.

It got it right this time, but.... Don't do that. Or if you must, be very cautious about believing the results the AI gives you - all it's doing is serving up the results of a glorified google search. This technology is enormously promising and already does all sorts of good things, but at the current state of the art using it will just get in the way of learning physics.

 

[PeterDonis]

The explanation using the earth-at-rest frame includes an unstated assumption about simultaneity.

So does the explanation using the traveler-at-rest frame; the unstated assumption just plays a somewhat different role in the explanation.

 

[Dale]

I was using AI to speed up my calc

Please don’t do that here. LLM’s are language models. They don’t do calculations and they don’t do physics. They just do language. Using them for physics is using them outside of their designed purpose. They will often give factually wrong answers written in grammatically correct and stylistically persuasive language, because that is all they are designed to do currently.

 

[Ibix]

Also sorry if I miscalculated the Lorentz factor, I was using AI to speed up my calc.

If you get to the wrong answer, have you really sped up? Also: use the right tool for the right job. Using a Large Language Model for algebra is like using a hammer to fit screws.

Also, are you using LLMs to try to learn relativity? That would probably explain a lot of your confusion. The kind of pedantic discrimination between frames' descriptions of a scenario that is vital to understanding this is not part of the way they work. So they are frequently spectacularly wrong - we've seen it several times on here.

Couldn't either the spaceship or the destination be chosen as a rest frame?

Strictly, no, because neither rocket nor stars are frames. If you mean "can I work this problem using the rest frame of the rocket or the rest frame of the stars", then yes, of course.

If you use the stars' rest frame, the distance between them is not length contracted (they are not moving) but the rocket's clocks tick slowly. It therefore takes the rocket $D/v$ to travel the distance $D$ between the stars at its speed $v$, but due to time dilation its clocks measure $D/(\gamma v)$.

If you use the rocket's rest frame the distance is length contracted to $D/\gamma$ and it therefore takes $D/(\gamma v)$ for the destination star to reach the rocket. The rocket's clocks tick normally in this frame, so there's no further correction needed.

We have the same answer for the elapsed time on the rocket using two different frames. Note that this is one of a very narrow class of problems that can be solved using only length contraction and time dilation. You will generally need the Lorentz transforms.

 

[Chenkel]

If you get to the wrong answer, have you really sped up? Also: use the right tool for the right job. Using a Large Language Model for algebra is like using a hammer to fit screws.

Also, are you using LLMs to try to learn relativity? That would probably explain a lot of your confusion. The kind of pedantic discrimination between frames' descriptions of a scenario that is vital to understanding this is not part of the way they work. So they are frequently spectacularly wrong - we've seen it several times on here.

Strictly, no, because neither rocket nor stars are frames. If you mean "can I work this problem using the rest frame of the rocket or the rest frame of the stars", then yes, of course.

If you use the stars' rest frame, the distance between them is not length contracted (they are not moving) but the rocket's clocks tick slowly. It therefore takes the rocket $D/v$ to travel the distance $D$ between the stars at its speed $v$, but due to time dilation its clocks measure $D/(\gamma v)$.

If you use the rocket's rest frame the distance is length contracted to $D/\gamma$ and it therefore takes $D/(\gamma v)$ for the destination star to reach the rocket. The rocket's clocks tick normally in this frame, so there's no further correction needed.

We have the same answer for the elapsed time on the rocket using two different frames. Note that this is one of a very narrow class of problems that can be solved using only length contraction and time dilation. You will generally need the Lorentz transforms.

Thanks for that analysis, I like how you uses two different reference frames and came up with the same elapsed time for the rocket.

I have been using many different things to learn relativity, and sometimes LLMs give helpful responses but like it has been said here, they're not always reliable so I use them with caution.

 

[PeterDonis]

sometimes LLMs give helpful responses

No, sometimes LLMs give responses that someone who doesn't already know the subject might think are helpful--but which are actually not.

but like it has been said here, they're not always reliable so I use them with caution.

You should not use them at all if you are trying to learn relativity (or any scientific theory, for that matter). That is simply not what they're for.

 

[Dale]

I have been using many different things to learn relativity, and sometimes LLMs give helpful responses but like it has been said here, they're not always reliable so I use them with caution.

In the same fashion sometimes automobiles may be helpful for baking cookies but they are not always reliable so use them with caution.

 

[Ibix]

sometimes LLMs give helpful responses

How do you evaluate whether the answers are correct or not if you don't already know the material?

I know LLMs are a new and shiny tool, but they're really not ready to do physics education yet.

 

[Chenkel]

How do you evaluate whether the answers are correct or not if you don't already know the material?

I know LLMs are a new and shiny tool, but they're really not ready to do physics education yet.

LLMs find patterns in language so sometimes that can be useful for finding common usage of certain terms in the field.

 

[Chenkel]

How do you evaluate whether the answers are correct or not if you don't already know the material?

I know LLMs are a new and shiny tool, but they're really not ready to do physics education yet.

I sometimes don't know if the material I get from an LLM is correct so I double check on wikipedia and physics forums or some authoritative third party if I can.

 

[Chenkel]

How do you evaluate whether the answers are correct or not if you don't already know the material?

I know LLMs are a new and shiny tool, but they're really not ready to do physics education yet.

Also sometimes you can get the LLM to admit where it's wrong to get a little critical thinking going.

 

[Dale]

I sometimes don't know if the material I get from an LLM is correct so I double check on wikipedia and physics forums or some authoritative third party if I can.

For learning physics, just skip use of LLM’s for now. Maybe in the future they will be useful, but currently they are actively harmful for physics education. Just like baking a cookie on an engine block is actively harmful.

In any case, this thread is now more about LLM’s than relativity. LLM-based posts are not acceptable on PF. Thread closed