Solving the Mystery of Simultaneity: A Relativity Question

[TheQuestionGuy14]

Hey! So basically I studied General Relativity for a while and was moving on to Special Relativity and there's one thing in it that I can't seem to understand, simultaneity.

So I've seen videos explaining it with a train, an observer in the moving train and an observer outside the train as the train gets struck by two lightning bolts. I understand how they see the events differently and are both right as time is dilated as light must always travel at the same speed. I get that, but when you take light out of the equation, and make it a larger distance, I really get confused, here's an example:

So, if you watch the video, there is a man and an alien, many millions of lightyears apart. When they are stationary, time moves the same relative to each other, yet when the alien cycles away, his 'now' is now our 200 years ago. How does this make sense? How can alien or any being far away deciding to take a cycle make their now so different to ours? Also if his now is our 200 years ago, has he just time traveled technically? Sorry if this sounds like madness but it really confuses me.

I hope someone here would be able to help me!

 

[FactChecker]

Suppose the alien is cycling and synchronizes his clocks (where he is and all the way to us) using a light beam and adjusting his distant clocks taking the speed of light into account. Because he still measures the speed of light as c, even though he is moving, we would think that he has made the wrong adjustments for light speed and that his clocks are not really synchronized correctly. The alien's definition of 'now' is according to when his clocks read the same time. But we disagree with how he set his clocks. So we do not agree with the alien on whether events are simultaneous. Notice that if events happen in the same position in the direction of relative motion, then we would agree with the alien about whether they are simultaneous. Our disagreement would grow as the events get farther apart in the direction of relative motion.

When you say that "his now is our 200 years ago, has he just time traveled technically?", you are talking about "his now" very far away from him. His clocks were synchronized using the speed of light, so it is impossible for him to go back in time because it is impossible to go faster than light.

 

[TheQuestionGuy14]

Suppose the alien is cycling and synchronizes his clocks (where he is and all the way to us) using a light beam and adjusting his distant clocks taking the speed of light into account. Because he still measures the speed of light as c, even though he is moving, we would think that he has made the wrong adjustments for light speed and that his clocks are not really synchronized correctly. The alien's definition of 'now' is according to when his clocks read the same time. But we disagree with how he set his clocks. So we do not agree with the alien on whether events are simultaneous. Notice that if events happen in the same position in the direction of relative motion, then we would agree with the alien about whether they are simultaneous. Our disagreement would grow as the events get farther apart in the direction of relative motion.

When you say that "his now is our 200 years ago, has he just time traveled technically?", you are talking about "his now" very far away from him. His clocks were synchronized using the speed of light, so it is impossible for him to go back in time because it is impossible to go faster than light.

Sorry, I still don't fully understand how he sees our past, then just by turning, he sees our future. I always thought that he would only be able to see the past, as the light would take time to reach him. (Eg. If he is 3 billion light years away, he sees Earth only 1 billion years old). I still don't see how the simple change of movement can make him see past and future. Could you explain it in layman's terms if ok? Thanks.

 

[Orodruin]

then just by turning, he sees our future

No he doesn't. You are confusing what the alien actually sees with what (once the signal reaches him) he can conclude happened and at what times. The point is that you and the alien (at the time you have assigned as "now" according to your rest frame) have space-like separation. In essence, this means that there is no objective way of determining whether you are in the alien's future or if he is in yours. There will always be a reference frame in which you are at the same time. In relativity, "now" has no universal meaning. The only thing that has universal meaning for two events A and B are the mutually exclusive options (1) A is in the future light-cone of B, (2) B is in the future light-cone of A, or (3) A and B have space-like separation, by some authors referred to as A being elsewhere from B.

In case (1), a signal from event B can reach event A and therefore affect it and vice versa for (2). For case (3), there is no way that the events A and B can affect each other. A signal from A to B or vice versa would have to travel faster than the speed of light.

 

[TheQuestionGuy14]

No he doesn't. You are confusing what the alien actually sees with what (once the signal reaches him) he can conclude happened and at what times. The point is that you and the alien (at the time you have assigned as "now" according to your rest frame) have space-like separation. In essence, this means that there is no objective way of determining whether you are in the alien's future or if he is in yours. There will always be a reference frame in which you are at the same time. In relativity, "now" has no universal meaning. The only thing that has universal meaning for two events A and B are the mutually exclusive options (1) A is in the future light-cone of B, (2) B is in the future light-cone of A, or (3) A and B have space-like separation, by some authors referred to as A being elsewhere from B.

In case (1), a signal from event B can reach event A and therefore affect it and vice versa for (2). For case (3), there is no way that the events A and B can affect each other. A signal from A to B or vice versa would have to travel faster than the speed of light.

So basically when the alien cycles away from Earth the events in 1817 on Earth become simultaneous with his, according to the video, does this mean that if he somehow used a wormhole, he could in theory see our past?

 

[Orodruin]

There are no wormholes in SR.

 

[PeterDonis]

How does this make sense?

Because "now" has no physical meaning. The two different "nows" don't correspond to anything actually changing, physically; they're just two different arbitrary lines drawn on spacetime.

does this mean that if he somehow used a wormhole, he could in theory see our past?

Wormholes are a whole different concept, which involves curved spacetime and can't even be analyzed using special relativity. As such, they are off topic for this thread. You need to understand SR itself first.

 

[PeroK]

So basically when the alien cycles away from Earth the events in 1817 on Earth become simultaneous with his, according to the video, does this mean that if he somehow used a wormhole, he could in theory see our past?

If this alien is millions of light years away and he can turn a powerful telescope on Earth then he would see things as they were millions of years ago. Seeing our past in this sense isn't a problem.

This example of simultaneity always seems to me to be designed to confuse rather than elucidate.

There's a post of mine from yesterday where I described the relativity of simultaneity in simple terms.

If you can't find it, I can always repost it here.

 

[Orodruin]

This example of simultaneity always seems to me to be designed to confuse rather than elucidate.

It is Brian Greene - it is designed to shock, awe, and sell, not to teach or clarify.

 

[TheQuestionGuy14]

If this alien is millions of light years away and he can turn a powerful telescope on Earth then he would see things as they were millions of years ago. Seeing our past in this sense isn't a problem.

This example of simultaneity always seems to me to be designed to confuse rather than elucidate.

There's a post of mine from yesterday where I described the relativity of simultaneity in simple terms.

If you can't find it, I can always repost it here.

Please do repost, thanks!

 

[FactChecker]

He is just seeing what our clocks at a distant location say is in the past, or what our clocks at a distant location say is in the future. We would say that his clocks are wrong.

Regarding his seeing "the future", he can not see anything till after it has actually happened according to our clocks. Remember that in that far distant direction, his clocks reach his "now" time much earlier than ours. And in the other distant direction, his "now" clocks are set much later than ours. (Or is it the opposite. I have trouble keeping it straight.)

 

[TheQuestionGuy14]

He is just seeing what our clocks at a distant location say is in the past, or what our clocks at a distant location say is in the future. We would say that his clocks are wrong.

Regarding his seeing "the future", he can not see anything till after it has actually happened according to our clocks. Remember that in that far distant direction, his clocks do not reach his "now" time till much later than ours.

So let's say the alien is 3 billion light years away, and then starts to move towards the Earth. So if he starts moving towards Earth, his transition to a new reference frame means that time dilates and length contracts - as soon as he starts moving, it is no longer 3 billion light years to Earth, but, say, 2 billion light years.

Before, he would have physically seen a clock saying "2017 minus 3 billion years" and, knowing he was 3 billion light years away, would conclude that it is now 2017. Now he's moving, it's only 2 billion light years to Earth, so he must conclude that, because he still physically sees "2017 minus 3 billion years", that it must now be 2017 minus a billion years (i.e. 2 billion years later than the time on the clock he sees).

Would this be correct?

 

[PeroK]

Please do repost, thanks!

If you have a vehicle with a light source in the middle, then in the reference frame of tge vehicle the light reaches the front and rear at the same time.

But, in a frame where the vehicle is moving, the light reaches the rear first - as it is moving towards the source and the front is moving away from the source.

Therefore, simultaneity is frame dependent.

 

[TheQuestionGuy14]

No he doesn't. You are confusing what the alien actually sees with what (once the signal reaches him) he can conclude happened and at what times. The point is that you and the alien (at the time you have assigned as "now" according to your rest frame) have space-like separation. In essence, this means that there is no objective way of determining whether you are in the alien's future or if he is in yours. There will always be a reference frame in which you are at the same time. In relativity, "now" has no universal meaning. The only thing that has universal meaning for two events A and B are the mutually exclusive options (1) A is in the future light-cone of B, (2) B is in the future light-cone of A, or (3) A and B have space-like separation, by some authors referred to as A being elsewhere from B.

In case (1), a signal from event B can reach event A and therefore affect it and vice versa for (2). For case (3), there is no way that the events A and B can affect each other. A signal from A to B or vice versa would have to travel faster than the speed of light.

So, all in all, by the time he reaches us it will be our present, and his present anyways. The video title doesn't really mean that the past and future are mixed with the present. The past is gone, but the alien can see it from Earth's light and the future is still yet to come, and he will only see it once it happens, causality and all preserved.

 

[Orodruin]

and he will only see it once it happens

He will see it even later due to the signal not arriving instantaneously.

 

[PeroK]

@TheQuestionGuy14

In fact, if you consider that the alien planet is orbiting its star as ours does and the relative velocity between the two planets is constantly changing, then you can see the fatuousness of reading any physical significance into an alien or earthling getting on a bicycle!

 

[jartsa]

So let's say the alien is 3 billion light years away, and then starts to move towards the Earth. So if he starts moving towards Earth, his transition to a new reference frame means that time dilates and length contracts - as soon as he starts moving, it is no longer 3 billion light years to Earth, but, say, 2 billion light years.

Before, he would have physically seen a clock saying "2017 minus 3 billion years" and, knowing he was 3 billion light years away, would conclude that it is now 2017. Now he's moving, it's only 2 billion light years to Earth, so he must conclude that, because he still physically sees "2017 minus 3 billion years", that it must now be 2017 minus a billion years (i.e. 2 billion years later than the time on the clock he sees).

Would this be correct?

Well I don't see any error. But in that story the now-moment on Earth according to he alien changed towards the past. That is a 'wrong' direction.Let's say the alien starts to cycle towards the Earth, and let's say that causes the now-moment on Earth according to he alien to change 200 years towards the future. Now we can conclude some things about the light the alien is seeing. Like how long time the light has been traveling according to the alien. Or maybe rather how much the travel time changed when the cycling motion started.

The received light quite suddenly became 200 years older according to the alien. As light received from the Earth became 200 years older according to the alien, that means the event on Earth that the alien is seeing became 200 years older according to the alien. And that means that all other events on Earth became 200 years older too, according to the alien. And that means that the Earth moved 200 years towards the future, according to the alien.

We, or the alien rather, can find a cause for that increase of age of light. It can not be anything else but 200 light years more distance for the light to travel.

 

[FactChecker]

Acceleration and deceleration adds some complications to the problem. Suppose the alien is already moving fast and decides to accelerate at time t=1 throughout his reference frame. Remember that we do not agree with him that his time t=1 is synchronized correctly. We see the trailing end of his reference frame accelerate earlier than at the alien's location and the front end accelerates later. That agrees with the shortening of his length measurements (in our eyes). It gets complicated. Apparently, people who are good with Minkowski diagrams (I am not one) can use them to keep track of everything.

 

[Mister T]

So I've seen videos explaining it with a train, an observer in the moving train and an observer outside the train as the train gets struck by two lightning bolts. I understand how they see the events differently and are both right as time is dilated as light must always travel at the same speed.

Perhaps I have a misunderstanding, but I don't see how time dilation is involved in those examples.

They do demonstrate that events that are simultaneous in one frame are not simultaneous in another, but I don't see how time dilation is involved in those explanations.