Does Time Dilation Occur in a Perfectly Circular Orbit at Near-Light Speed?

[Arkalius]

Can you give an example of faster than light signaling that will create reference frame in which the signal arrived before it was sent ?

Let's say I'm here on Earth you're on your ship about a light year away traveling away from Earth with some speed. I send you an instantaneous signal when my clock says it's 1100. At this instant for me, your clock says, say 1340. You get this signal at 1340 your time. However, due to the fact that you're moving relative to me, and the relativity of simultaneity, for you at the instant your clock says 1340, my clock says it's 0300. So, you send an instantaneous signal back to me, and it arrives to me before I ever sent one to you. Of course, for me, when the time was 0300, your time was something like 0600, so I can respond back asking about this bizarre message I receive from you, and then you're confused because that comes before you ever replied to my first one, and this keeps going.

Keep in mind here the numbers are just arbitrary, but the effect they're pointing to is real. The concept of "now" is relative. There is no universal instant that everyone shares.

This effect can still happen with non-instantaneous signals that travel faster than light, but this puts a lower bound on the speed at which the target of the signal must be traveling away from you for it to happen. The faster the signal, the less this lower bound is. That bound basically uses the velocity addition formula for doubling the velocity. So the lower bound for velocity $v$ a frame must be traveling away from you for a signal that moves at faster than light velocity $k$ such that it could repeat that signal back to you so that it arrives before it was sent is given by $v = \frac {2k} {1 + k^2}$

So, if you could send signals at twice the speed of light, the target has to be moving away from you faster than 0.8c to send it back to you before you sent it. If you can send it at 10x the speed of light, the target only has to be moving away faster than about 0.198c. You'll see that as $k$ approaches infinity (instant communication), $v$ approaches 0.

How much further in the past the return signal will go depends both on how much faster than the lower bound the target is moving and how far from you they are.

 

[Steeve Leaf]

Decent article. The comments might be subtitled "fifty ways to miss the point", though.

Some of the comments are from Rich the writer himself and some others are interesting and informative I didn't go through all of them( did you ? ) so maybe fifty is the right figure , ☺

 

[Steeve Leaf]

Let's say I'm here on Earth you're on your ship about a light year away traveling away from Earth with some speed. I send you an instantaneous signal when my clock says it's 1100. At this instant for me, your clock says, say 1340. You get this signal at 1340 your time. However, due to the fact that you're moving relative to me, and the relativity of simultaneity, for you at the instant your clock says 1340, my clock says it's 0300. So, you send an instantaneous signal back to me, and it arrives to me before I ever sent one to you. Of course, for me, when the time was 0300, your time was something like 0600, so I can respond back asking about this bizarre message I receive from you, and then you're confused because that comes before you ever replied to my first one, and this keeps going.

Keep in mind here the numbers are just arbitrary, but the effect they're pointing to is real. The concept of "now" is relative. There is no universal instant that everyone shares.

This effect can still happen with non-instantaneous signals that travel faster than light, but this puts a lower bound on the speed at which the target of the signal must be traveling away from you for it to happen. The faster the signal, the less this lower bound is. That bound basically uses the velocity addition formula for doubling the velocity. So the lower bound for velocity $v$ a frame must be traveling away from you for a signal that moves at faster than light velocity $k$ such that it could repeat that signal back to you so that it arrives before it was sent is given by $v = \frac {2k} {1 + k^2}$

So, if you could send signals at twice the speed of light, the target has to be moving away from you faster than 0.8c to send it back to you before you sent it. If you can send it at 10x the speed of light, the target only has to be moving away faster than about 0.198c. You'll see that as $k$ approaches infinity (instant communication), $v$ approaches 0.

How much further in the past the return signal will go depends both on how much faster than the lower bound the target is moving and how far from you they are.

I don't have to be there physically do I ? We can replace me with a device that just return the information back to us at Earth, don't tell nobody about it and make a lot of money. We tried to get patent on it but every time at appears that it already patented .
I think that the problem here is first to receive the signal of FTL radiation/interaction than work on not breaking causality if it is in danger. Suddenly causality becomes a FORCE a fifth one.

 

[Ibix]

Some of the comments are from Rich the writer himself and some others are interesting and informative I didn't go through all of them( did you ? ) so maybe fifty is the right figure , ☺

I didn't go through them all. The author's were good, but a lot of the time he was replying to say "no, you've missed the point". And note the comment he added at the top of the article. Maybe there are insightful comments, but they seem to be a bit lost in the noise.