Light travel paradox? Please, help to figure it out

[Alexroma]

I need your help to figure it out if the following thought experiment makes sense. Imagine two points in space at the same distance from Earth, 100 light years. At one point a previously unknown supernova explodes; we observe it’s bright light in the sky for several months, and after that it fades away. From another point, a super-luminous object comes to us at a near-light speed, and it’s so bright that it’s visible to us through all its way to Earth for almost 100 years. Isn’t there a paradox that we can observe a flash of light only when it reaches us, but in case of the objects coming to us with near-light speed, we can observe them on all their way to us? … or can’t we? In other words, is there a principal difference between travel of light and travel of luminous objects?

 

[HourBee]

I don't see any paradox here. We see the light when it reaches us in both cases. The movement of this super-luminous object isn't going to make the light reach us faster, so I fail to see the contradiction when one of the key factors is completely irrelevant. Please do say if I'm missing something.

 

[Alexroma]

The difference is that we can not observe the actual travel of a light flash. Or may be it's just me? Anybody sees the difference?

 

[HourBee]

The difference is that we can not observe the actual travel of a light flash. Or may be it's just me? Anybody sees the difference?

We could observe the path of the light (from somewhere other than Earth, that is) in both cases. The fact that the length of the lighted period is different doesn't make the light behave any differently. If I turn off a lamp immediately after I turn it on, the light isn't any different than light from the lamp when it's on for a few minutes.

 

[DaveC426913]

a super-luminous object comes to us at a near-light speed, and it’s so bright that it’s visible to us through all its way to Earth for almost 100 years. Isn’t there a paradox that we can observe a flash of light only when it reaches us, but in case of the objects coming to us with near-light speed, we can observe them on all their way to us? … or can’t we? In other words, is there a principal difference between travel of light and travel of luminous objects?

If the spaceship left its home 100 light years away 100 years ago, we would not see the light of it leaving its planet until 100 years has passed - just like the star.

No part of the spaceship's journey would be visible before 100 years has passed.

I see no paradox either.

The difference is that we can not observe the actual travel of a light flash. Or may be it's just me? Anybody sees the difference?

You cannot observe the actual travel of a spaceship either - you only observe the light from it, which makes the journey no faster than the light from the star.

 

[Alexroma]

If the spaceship left its home 100 light years away 100 years ago, we would not see the light of it leaving its planet until 100 years has passed - just like the star.

That puzzles me, I'll show you why. Suppose, you have synchronized clocks at two close to each other points, both 100 l.y. away. At the same moment, they send to Earth a light flash from one point and from another point - a super-luminous object, traveling at such near-light speed that it takes 100 years and 1 day for it to reach Earth. In 100 years you observe on Earth the light flash coming from the first point and an image of the super-luminous object just leaving the other point. In the first case, it's all clear. But in the second case, there is only one day between the observation of the super-luminous object at starting point and it's reaching the Earth. Isn't it paradoxical that you observe this object covering the distance of 100 l.y. in just one day?

 

[phinds]

Isn't it paradoxical that you observe this object covering the distance of 100 l.y. in just one day?

Huh? Where's the paradox? The fact that an object shows up on your doorstep after a 100 year journey doesn't seem to be much of a paradox, just because it happens that you just recently found out that he started out 100 years ago.

 

[Alexroma]

Suppose that in the same thought experiment there is another “non-enlightened” observer who observes only the second point and knows only the distance to it (100 l.y.), without knowing the moment when the super-luminous object started to move. When this second observer sees the start of that object, he naturally expects it to come to Earth in more than 100 years, but surprise! The object actually comes the next day!

How comes that for the enlightened observer this object goes with the near-light speed, and for the non-enlightened observer - much faster than the speed of light?

 

[Janus]

Suppose that in the same thought experiment there is another “non-enlightened” observer who observes only the second point and knows only the distance to it (100 l.y.), without knowing the moment when the super-luminous object started to move. When this second observer sees the start of that object, he naturally expects it to come to Earth in more than 100 years, but surprise! The object actually comes the next day!

How comes that for the enlightened observer this object goes with the near-light speed, and for the non-enlightened observer - much faster than the speed of light?

Your "non-enlightened" observer would come to the same conclusion as your "enlightened" observer. The fact that the object arrives one day after he first sees it at 100 ly away tells him that it was traveling towards him at near light speed. The object will be following close behind the light of that first image. That, and the fact that the light from the object will be extremely blue-shifted. He will see 100 yrs of light emitted from the object compressed ito one day.

Nothing about this is paradoxical.

 

[phinds]

Alexroma, you seem DETERMINED to set up a paradox where there is none. There isn't. Get over it.

I'm sorry if this sounds harsh. I don't really mean to be, but your apparent refusal to believe what everyone is telling you is the cause for my statement.

 

[Alexroma]

The object will be following close behind the light of that first image. That, and the fact that the light from the object will be extremely blue-shifted. He will see 100 yrs of light emitted from the object compressed ito one day. Nothing about this is paradoxical.

OK, thank you! That explains everything. I was thinking about it, but I was not sure.

 

[DaveC426913]

But in the second case, there is only one day between the observation of the super-luminous object at starting point and it's reaching the Earth. Isn't it paradoxical that you observe this object covering the distance of 100 l.y. in just one day?

I don't see this as a problem at all.

A relativistically traveling spaceship is following closely behind its own light.

When it was 100ly away its light took 100ly to reach us. When it's 100 miles way, it light takes microseconds to reach us.

Yep. It would appear to take only one day from start of journey to arrival. This makes sense. We know the source of light it is in motion.

 

[Alexroma]

Alexroma, you seem DETERMINED to set up a paradox where there is none. There isn't. Get over it.

I am not that "DETERMINED" (see my previous post). Thank you for the explanations!

 

[BobG]

In other words, is there a principal difference between travel of light and travel of luminous objects?

Alexroma, you seem DETERMINED to set up a paradox where there is none. There isn't. Get over it.

I'm sorry if this sounds harsh. I don't really mean to be, but your apparent refusal to believe what everyone is telling you is the cause for my statement.

That does seem harsh. The question(s) is whether is a difference between light from a stationary object and light from a moving object (even though the question may not have been well enough formed to make that obvious), and if there isn't a difference, then doesn't that create a paradox?

There is a difference, as Janus explained. The light from the traveling object undergoes a Doppler shift.

 

[Alexroma]

There is a difference, as Janus explained. The light from the traveling object undergoes a Doppler shift.

Thank you, BobG! Now I completely got it: there is really a difference, but it's not paradoxical.

 

[Alexroma]

BTW, as I understand, this difference between travel of light and and travel of luminous objects with near-light speed is fundamentally explained by the wave function of light. Am I right?

 

[DaveC426913]

BTW, as I understand, this difference between travel of light and and travel of luminous objects with near-light speed is fundamentally explained by the wave function of light. Am I right?

You don't need to invoke anything so fancy; it is simple geometry.

See attached diagram.
Take a piece of card, like a playing card.
Hold up to your screen with its left edge on the Y-axis.
Sweep the card slowly to the right.
Observe what happens.

 

[Alexroma]

Thanks to all the valuable input here, I figured out a new way to calculate the special relativistic time dilation factor (if it’s new only to me, please, let me know). I posted it in Relativity section of the forum, as it looks to belong more there:

https://www.physicsforums.com/showthread.php?t=543550

 

[DaveC426913]

As posted in your other thread, it is also relevant here:

You seem to be confusing two things here. Maybe it's just your terminology.

The approach and recession of an object at relativistic speeds has nothing to do with time dilation.

You would see the same effect if you examined your craft's flight using classical Newtonian mechanics.