Conceptualizing travel toward a light source

[teachmemore]

I apologize if this topic has been discussed before. Although it seems basic enough, I failed to find any discussion on it.

I just can't seem to make sense of this simple thought experiment - traveling toward a light source.

Lets say there was a star 1 light year away from Earth and I traveled to it at a speed near c, so that I came within a second of the star, at my given speed.

From Earth's frame of reference, it has taken me 1 year to reach the star.

Now I am sitting outside the star and viewing it in real-time, but the people on Earth are seeing it as it was 1 year ago.

At the time I left earth, I was viewing the star as it was 2 years prior to what I am viewing of the star in my present position.

So as I was traveling towards the star, I watched the star age by 2 years? But for the people on earth, in their reference frame it only aged by 1 year?

Is this correct?

 

[Grep]

Forgive me if I make a mistake here, I'm light-headed because I'm hungry. But let's see if we can see where you made a mistake.

I apologize if this topic has been discussed before. Although it seems basic enough, I failed to find any discussion on it.

I just can't seem to make sense of this simple thought experiment - traveling toward a light source.

Lets say there was a star 1 light year away from Earth and I traveled to it at a speed near c, so that I came within a second of the star, at my given speed.

From Earth's frame of reference, it has taken me 2 years to reach the star.

Now I am sitting outside the star and viewing it in real-time, but the people on Earth are seeing it as it was 1 year ago.

At the time I left earth, I was viewing the star as it was 2 years prior to what I am viewing of the star in my present position.

That 2 years would be the time people on Earth would experience. Not you. You experience time dilation relative to the Earth and Star, and so less time has passed for you than on the Earth and at the star. Of course, you would feel less than 2 years pass, but you also would say the star was less than 1 light year away (in your frame of reference) due to Lorentz contraction as you were travelling. So everything would seem to work out logically for you.

So as I was traveling towards the star, I watched the star age by 2 years? But for the people on earth, in their reference frame it only aged by 1 year?

Is this correct?

In short, you saw it age for less than 2 of your own years, though you could calculate that it is now 2 years older in it's own frame of reference and the Earth's. People on Earth would indeed see it age by 2 years, though the light when you left was 1 year old, and the light when you get there is 1 year old. But it's still a difference of 2 years. Remember you said 2 years pass in the Earth's frame of reference. But then you disregard that information, and decided that 2 years pass for you, which is false. And the amount of time experienced by the star would be different from the amount of time you would experience.

I hope that's clear and that I didn't mess up the explanation...

 

[teachmemore]

Forgive me if I make a mistake here, I'm light-headed because I'm hungry. But let's see if we can see where you made a mistake.

That 2 years would be the time people on Earth would experience. Not you. You experience time dilation relative to the Earth and Star, and so less time has passed for you than on the Earth and at the star. Of course, you would feel less than 2 years pass, but you also would say the star was less than 1 light year away (in your frame of reference) due to Lorentz contraction as you were travelling. So everything would seem to work out logically for you.

In short, you saw it age for less than 2 of your own years, though you could calculate that it is now 2 years older in it's own frame of reference and the Earth's. People on Earth would indeed see it age by 2 years, though the light when you left was 1 year old, and the light when you get there is 1 year old. But it's still a difference of 2 years. Remember you said 2 years pass in the Earth's frame of reference. But then you disregard that information, and decided that 2 years pass for you, which is false. And the amount of time experienced by the star would be different from the amount of time you would experience.

I hope that's clear and that I didn't mess up the explanation...

Hi Grep. I appologize for making a small typo in my original entry. Only 1 year has passed from the Earth's frame of reference. (to make it simpler)

Your first comment on Lorenz contraction and time dilation was already obvious to me. That is not the issue I see with this scenario.

But there is a problem with what you describe here and for what I describe above. Firstly, you made a slight error, for if it had taken me two years from Earth's reference frame, I would now see the the star as it is 3 years from the time I looked at it on earth. (the 1 year delay to Earth + the 2 years of travel time). But let's say the trip only takes 1 year from Earth's reference frame.

Yes, As you point out, due to time dilation, less than 1 year passes in my frame of reference, but during that travel time, from my own frame of reference, am I not watching the star age? So that when I stop, and enter the stars frame of reference, I now see the star as being 2 years older than when I first looked at the star on earth?

How can I watch a star age by 2 years, while less than 1 year is passing for me within my reference frame? That is what doesn't make sense to me.

 

[pervect]

The short answer is "doppler shift". If you imagine the star emitting some light, the light will be shifted towards the blue spectrum of your approach by your velocity. However, pictures that the light carries will also be "sped up".

This is the raw, unprocessed, received data, and it's due to the reduction in travel times as you approach the star.

Doppler shift depends only on relative velocity - if someone was watching you on the star through a very large telescope, and if they didn't process the images in any way shape manner or form, they would also see you sped up.

I'm not sure if that helps, but I'm not sure why the existence of doppler shift should seem confusing. Unless you're confused about the relationship between doppler shift and time dilation?

 

[teachmemore]

The short answer is "doppler shift". If you imagine the star emitting some light, the light will be shifted towards the blue spectrum of your approach by your velocity. However, pictures that the light carries will also be "sped up".

This is the raw, unprocessed, received data, and it's due to the reduction in travel times as you approach the star.

Doppler shift depends only on relative velocity - if someone was watching you on the star through a very large telescope, and if they didn't process the images in any way shape manner or form, they would also see you sped up.

I'm not sure if that helps, but I'm not sure why the existence of doppler shift should seem confusing. Unless you're confused about the relationship between doppler shift and time dilation?

I was aware that under my scenario, doppler shift would occur. I just didn't think through the significance of this.

I understand now where my misunderstanding lay. Since the frequency of the light increases, more data can reach me, while light maintains the same relative velocity to my reference frame.

 

[Grep]

But there is a problem with what you describe here and for what I describe above. Firstly, you made a slight error, for if it had taken me two years from Earth's reference frame, I would now see the the star as it is 3 years from the time I looked at it on earth. (the 1 year delay to Earth + the 2 years of travel time). But let's say the trip only takes 1 year from Earth's reference frame.

I was talking about from the perspective of the Earth, not you, so no error there. But anyways, no worries. Pervect (someone likes the Myth Inc. books... hehe) got to the crux of the matter.

I would suggest you read post # 12 by AdamMc in this thread: https://www.physicsforums.com/showthread.php?t=444079 . It goes through it clearly and with real numbers, and shows what you would compute and what you would actually see, and how they interact. Excellent post to clear up this kind of thing and get it all straight in your head.

Fun working things out with SR, isn't it?

 

[teachmemore]

Thank you Grep. I'm certain I have it all nuances of SR clear now.