Exploring Time Dilation and Length Contraction with Alice's Spaceship

[MAYA]

This is my first post. :)
Here it goes...

Suppose alice's spaceship is traveling at speed close to c.. in line with a star. Because of length contraction she's going to find the distance towards it shorter than the "rest" distance. Does this mean she's going to get a closer look at the star (like looking through a telescope).

Since there is no theoretical limit on how closer she can get near to speed of light, there's no limit for length contraction too. (As long as the values are not exactly c and zero respectively)

The same idea in a different question is , if she is traveling in line with sun, is she going to feel more heat because of her apparent closeness to sun?

 

[xox]

This is my first post. :)
Here it goes...

Suppose alice's spaceship is traveling at speed close to c.. in line with a star. Because of length contraction she's going to find the distance towards it shorter than the "rest" distance. Does this mean she's going to get a closer look at the star (like looking through a telescope).

Since there is no theoretical limit on how closer she can get near to speed of light, there's no limit for length contraction too. (As long as the values are not exactly c and zero respectively)

The same idea in a different question is , if she is traveling in line with sun, is she going to feel more heat because of her apparent closeness to sun?

Welcome to the forum, Maya

To your questions:

1. You are correct, if Alice is measuring the distance [itex]L[/itex] when she is at rest wrt. the Sun, she will be measuring a shorter distance, [itex]L \sqrt{1-(v/c)^2}[/itex] when she travels at speed [itex]v[/itex].

2. Alice will also feel increased radiation, due to the Doppler effect. If the em waves from the Sun are of frequenct [itex]f_0[/itex] when Alice is at rest wrt. the Sun, the frequency increases to [itex]f_0 \sqrt{\frac{1+v/c}{1-v/c}}[/itex] when Alice flies in a straight line towards the Sun.

 

[Simon Bridge]

This is my first post. :)

Welcome to PF;

Suppose alice's spaceship is traveling at speed close to c.. in line with a star. Because of length contraction she's going to find the distance towards it shorter than the "rest" distance. Does this mean she's going to get a closer look at the star (like looking through a telescope).

Yes. The star is closer in Alice's rest frame.

By "in line with" I assume you mean Alice is traveling directly towards the star.
Is that correct?

It helps to be explicit about who you are comparing Alice to.
Say Bob is also traveling relativistically wrt the star but at a slower speed than Alice, and Oscar is at rest wrt the star. At some time t=0, Alice and Bob and Oscar are all at the same coordinate, x=0.

Now you can compare them properly.
Remember that as far as Alice, Bob, and Oscar are concerned, they are at rest, and everyone else, including the star, is moving. i.e. Alice will report that the star is moving towards her at speed v_A and Oscar is passing at that speed too... etc.

If Oscar sees the star distance R away, then Alice sees it a distance R/γ_A away and Bob sees it a distance R/γ_B away, where γ_B<γ_A, and γ_X=1/√(1-(v_X/c)²)

Since there is no theoretical limit on how closer she can get near to speed of light, there's no limit for length contraction too. (As long as the values are not exactly c and zero respectively)

Yes.
At t=0 by her clock, the nose of her ship may already be tickling the star's corona, provided the star is going fast enough.

There is a wrinkle about how you measure distances fast enough at those kinds of speeds.
Say she knows the diameter of the star, and keeps track of the angular diameter with the forward telescope.

The same idea in a different question is , if she is traveling in line with sun, is she going to feel more heat because of her apparent closeness to sun?

Yes, she's closer to the star.
But she's probably more worried about being so close to a gamma-ray object :)

 

[Nugatory]

Suppose alice's spaceship is traveling at speed close to c.. in line with a star. Because of length contraction she's going to find the distance towards it shorter than the "rest" distance. Does this mean she's going to get a closer look at the star (like looking through a telescope).

Closer than what? For any distance, there's some time at which she will be that distance from the star because she's moving towards it. So I'll try to firm up your question a bit... I think what you're really asking is:

Alice's spaceship is traveling at speed near c relative to the star. There is an observer (Bob) who is at rest relative to the star and who measures the distance between him and the star to be D. At the moment that Alice flies past Bob, Bob will correctly say that Alice's ship is at that moment also a distance D from the star. However, thanks to length contraction, Alice measures the distance to the star as she passes Bob to be less than D. Does this mean she's going to get a closer look at the star than Bob (like what Bob would see looking through a telescope)?

If that's what you're asking, the answer is no. The same light is hitting Alice's eyes and Bob's eyes (has to - they're both at the same point in space at that moment), and that that's what they see. Of course, if we wait just a moment after that, Alice will be much closer to the star (unlike Bob, she's moving towards it) and then she will have a better close-up view than Bob.

 

[dauto]

Yes and yes. Note that Alice is not only closer to the star. The radiation coming from the star will also be blue shifted which will increase the amount of incoming heat even more.

 

[Simon Bridge]

Curious - this is something that can mess up experienced people ... this is why it is important to be precise.

As far as Bob is concerned, Alice, next to him, is getting the same radiation he is.
But Alice, at the instant she sees Bob next to her? What does she see?

Is that the question?

 

[Nugatory]

Curious - this is something that can mess up experienced people ... this is why it is important to be precise.

As far as Bob is concerned, Alice, next to him, is getting the same radiation he is.
But Alice, at the instant she sees Bob next to her? What does she see?

Is that the question?

As long as "next to" means "at the same point in space", there are no simultaneity issues, only blue-shift and relativistic beaming.

 

[MAYA]

Welcome to the forum, Maya

Thanks :)

2. Alice will also feel increased radiation, due to the Doppler effect. If the em waves from the Sun are of frequenct [itex]f_0[/itex] when Alice is at rest wrt. the Sun, the frequency increases to [itex]f_0 \sqrt{\frac{1+v/c}{1-v/c}}[/itex] when Alice flies in a straight line towards the Sun.

Alice need not be traveling towards sun. She can be traveling away from sun also at a velocity v (wrt sun/bob on Earth frame of reference) and get the same length contraction factor. Only Alice will be looking at sun through her back-window. But now the doppler shift reverses and the frequency is now lower (compared to bob), which delivers lower energy radiation.

 

[MAYA]

Welcome to PF;

Thanks :)

By "in line with" I assume you mean Alice is traveling directly towards the star.
Is that correct?

Not really. Alice can be traveling towards or away from the star and she should get the same contraction wrt star-earth FOR. Or am I mistaken?

But she's probably more worried about being so close to a gamma-ray object :)

If she was going away from the sun, we don't have a gamma-ray object anymore. :)

My understanding is..

Bob who is at rest in Sun/Earth FOR, sees Alice at the distance 1AU at t=0. It is pretty simple, because Alice is next to him when t=0. He used his meter rods length 1m

Now Alice says she is also 1 AU from sun. She used her meter rods of 1 m (which bob claims to be contracted, which she doesn't need to care about anyway).

Now if there is indeed a higher radiation, there is no way Alice can explain it physically at the distance of 1 AU.

Maybe for her Sun's intensity is lower because her clocks are running slow (compared to bob)?

 

[MAYA]

Curious - this is something that can mess up experienced people ... this is why it is important to be precise.

As far as Bob is concerned, Alice, next to him, is getting the same radiation he is.
But Alice, at the instant she sees Bob next to her? What does she see?

Is that the question?

Exactly.

 

[WannabeNewton]

If that is the question then there will certainly be no magnification of the Sun as if looking through a telescope lens.

As Nugatory correctly pointed out, energy-wise there will be a doppler shift of the incoming radiation and optics-wise the phenomenon of relativistic beaming ("headlight effect") will take place.

EDIT: I would highly recommend downloading and playing around with the following program: http://gamelab.mit.edu/games/a-slower-speed-of-light/ as it will clearly illustrate the optical and dynamical effects of relativistic speeds.

 

[pervect]

One non-obvious thing. Though Alice will be closer to the star, and it will be brighter and blueshifted , it will appear smaller in the sky, not larger, due to the combined effects of stellar aberration and signal delay.

By "appear smaller" I mean it will subtend a smaller visual angle.

See for example http://www.anu.edu.au/physics/Searle/ - there are several visual examples. If you download the first video in the "downloads" section and play it, you'll see how the aberration effects make the destination appear to move away as you accelerate towards it due to the visual angle decreasing. There are 4 stages to the video, non-relativistic, aberration only, abberation + doppler shift, and abberation + doppler + intensity effects.

There is also a paper that describes the mathematical details on the website.

 

[jartsa]

Let's say there's bunch of sun rays, the directions of which Alice wants to study.

Moving away from the sun makes the difference of the directions of the rays larger, which makes it easy to measure the direction differences.

So maybe velocity away from the sun enlarges the picture of the sun?

 

[pervect]

So maybe velocity away from the sun enlarges the picture of the sun?

I haven't worked out the math but I believe that is correct. It will get dimmer, though.

 

[Dale]

Alice can be traveling towards or away from the star and she should get the same contraction wrt star-earth FOR. Or am I mistaken?

Contraction is indeed the same traveling towards or away, but there are other relativistic effects, such as Doppler and aberration. We discussed an interesting paper on this topic in a previous thread, I will see if I can dig it up.

Now if there is indeed a higher radiation, there is no way Alice can explain it physically at the distance of 1 AU.

Sure she can. The same laws of physics work in all frames. They are just different laws than you might have originally assumed. Those laws include Doppler and aberration as well as length contraction.

EDIT: here is the paper http://cartan.e-moka.net/content/download/248/1479/file/Astronave relativistica.pdf and here is the thread where we discussed a closely related topic https://www.physicsforums.com/showthread.php?t=696108