Confused about the logic of a Special Relativity problem

[Orodruin]

I should probably read Greene's book, which should have this thing much better explained than the TV show.

Oh, and there is another thing you should think about before you go out to buy Greene's book: All popular science will only teach you about science, it will not teach you science. It can teach you about relativity, but it will give you the flashy version with the paradoxes and similar stuff, presenting the problems and solutions in a flashy way that is designed to make you go "whoaaaooooooo" rather than to learn anything about the theory itself. A lot of the misconceptions that people come here to ask question about are based on overthinking popularised science and extending the analogues that the popularisers make far beyond their region of validity. Bottom line is: You will not learn relativity by watching or reading Brian Greene. In order to do so, you need to pick up an actual course in relativity. A (free) resource such as @bcrowell 's Relativity for Poets would be a much better place to start than a popular book.

 

[Nantes]

I do not get it, you have said yourself that you agree that it cannot see into the future. The light needs to reach it.

First, thanks for the relativity for poets link!

Yes, from an utility standpoint he cannot. But let me put some dates to try and clarify what I mean by seeing into the "future" (dates are from Earth's perspective):

Message asking the alien what's next's weeks' lottery number (for, according to the video, his "now" slice of the Earth is one of the future, which we are pretending to be one week here) is sent on December 14th, 2015
Alien one light year away receives message on December 7th, 2016 our time (because he's seeing Earth one week into the future, thus he'll receive our message one week earlier than we would expect him to). The timestamp on the message still says December 14th, 2015
It will still take one week for him to be able to see December 21th 2015's lottery numbers, which is what we asked him to relay to us
He'll send us December 21th 2015's lottery numbers on December 14th, 2016
We'll receive the numbers on December 14th, 2017

Because we received not "next week's" lottery numbers, but rather the lottery numbers of 1 year, 11 months and 3 weeks ago (that is, December 21th 2015), in practice the numbers are not from the future, but in reality we'd be able to conclude the alien really was seeing the future at that time, as by all rights we should have received the message with the numbers of December 21th 2015's lottery on December 21th 2017 if the alien could not see into the future.

All that is, of course, assuming the alien is stationary (he'd have to be moving in reality) and completely disregarding relativistic effects, and both things would have to be accounted for/compensated for the real experiment.

 

[Herman Trivilino]

but in reality we'd be able to conclude the alien really was seeing the future at that time,

Our future, not the future. There is no such thing as a universal future. There are things that are in our future but in his past.

And he saw what would become our future, but he didn't see it until after it had already happened to us.

 

[Orodruin]

What you are seeing is really nothing else than the fact that "now" is not really well defined in relativity.

All that is, of course, assuming the alien is stationary (he'd have to be moving in reality) and completely disregarding relativistic effects, and both things would have to be accounted for/compensated for the real experiment.

This is also not really possible. You cannot cherrypick which relativistic effects you consider and you certainly cannot ignore that something is moving when it has to.

 

[Herman Trivilino]

This is also not really possible. You cannot cherrypick which relativistic effects you consider and you certainly cannot ignore that something is moving when it has to.

The video purposely chooses a scenario where the speed of the observer is nonrelativistic so that relative simultaneity is the only relativistic effect. The alien is many many light years away from our galaxy, if I recall correctly. I didn't watch the video recently, but I remember it. I thought that particular piece of it was well done.

In other words, the Lorentz transformation equation $\Delta t'=\gamma(\Delta t-\beta \Delta x)$ doesn't become $\Delta t'=\Delta t$ in the limit of low speed if $\Delta x$ is very very large.

 

[Orodruin]

This still does not let you ignore velocity, in the time it takes the light to arrive you will move a very long distance even at velocities much slower than the speed of light.

 

[Ibix]

The alien can't see the future. If it's one light year away and at rest with respect to us, it'll say that now it's December 2015 on Earth. But looking through a telescope it sees December 2014, because that's the light that's reached it. If it then accelerates instantaneously to extremely high speeds, it can say that now it's December 2016 on Earth. But if it looks through the telescope, all it sees is December 2014, because that's the light that's reached it.

In relativity there is a degree of flexibility in what I call "now" anywhere except right where I am. That flexibility comes from the fact that nothing can travel faster than light, so nothing can affect anything until light gets there. Some authors have, I gather, chosen to split things into "the future", which is things that can be affected by my actions here-and-now, "the past", which is things that can have affected me here-and-now, and "elsewhere", which is things that can neither affect nor be affected by me here-and-now. "Now-but-not-here" is a part of "elsewhere", but which part turns out to depend on an arbitrary definition (the "Einstein simultaneity convention", typically) - so which bits of "elsewhere" happened before and after "now" is also an arbitrary definition. It has no physical significance.

 

[Nantes]

If it then accelerates instantaneously to extremely high speeds, it can say that now it's December 2016 on Earth. But if it looks through the telescope, all it sees is December 2014, because that's the light that's reached it.

Why would he say it's December 2016 on Earth if he's still seeing the same December 2014?

 

[Nugatory]

Why would he say it's December 2016 on Earth if he's still seeing the same December 2014?

If something happens one light-year away from me, light from that event will reach my eyes one year after it happened. What is happening there now is what I'm going to see in one year, and what I'm seeing now is what happened one year ago.

So when I say "it is December 2016 on earth", I'm saying "earth is X light-years away from me, and if a flash of light left Earth right now, that flash of light will reach me and I will see calendars on Earth turned to December 2016 on December 2016+X". It's the exact same logic that I'm using when I say at 11:00 AM "I hope you're leaving your house now" when your house is 100 kilometers away, your car moves at 100 km/hr, and we've agreed to meet at noon; and that I'm using when we meet up at noon and I can say "You're here now so I know you did leave your house at 11:00 AM".

 

[Ibix]

Why would he say it's December 2016 on Earth if he's still seeing the same December 2014?

Beaten to the punch by Nugatory, but why would the aline say the time on Earth is what it can see? It's perfectly aware of the speed of light. Saying "it's December 2014 because I can see their calendars say December 2014" would be daft - it's like saying that the batter hit the ball and a fraction of a second later the bat and ball made a loud crack sound. It makes much more sense to say the bat and ball made a loud crack sound at the moment of impact, but it took a fraction of a second for the sound to reach me. Similarly, one light year away, we know the information is a year out of date. Why would we (or the alien) say that "now" is what we see?

 

[Nantes]

If something happens one light-year away from me, light from that event will reach my eyes one year after it happened. What is happening there now is what I'm going to see in one year, and what I'm seeing now is what happened one year ago.

So when I say "it is December 2016 on earth", I'm saying "earth is X light-years away from me, and if a flash of light left Earth right now, that flash of light will reach me and I will see calendars on Earth turned to December 2016 on December 2016+X". It's the exact same logic that I'm using when I say at 11:00 AM "I hope you're leaving your house now" when your house is 100 kilometers away, your car moves at 100 km/hr, and we've agreed to meet at noon; and that I'm using when we meet up at noon and I can say "You're here now so I know you did leave your house at 11:00 AM".

Yeah, I already knew that. I recognize now my question was ambiguous, sorry for that! What I meant was this: Ibix says the aliens knows it's 2015 on Earth, despite seeing 2014, because he knows he's one light year away. All perfectly fine thus far. Then he mentions the alien "accelerates instantaneously to extremely high speeds", still sees 2014 for some reason, but now suddenly we're in 2016? If he accelerated, he moved. If he moved, he can't be seeing December 2014 anymore! If he's still seeing December 2014, he hasn't moved much at all, so why did the year suddenly leap ahead to 2016?

Is it because he's now in a transversal slice of the space time loaf of bread like Greene's video shows, and at his current point the present time is still the same, but the future-seeing effect is magnified through the distance from Earth?

Goddamn it, this dang's confusing.

 

[Ibix]

He hesn't moved much (yet) - the acceleration is instantaneous. But in accelerating, he's changed his definition of "now, on Earth" from December 2015 to December 2016. He could immediately reverse acceleration and come to rest relative to Earth again (albeit a bit closer) and revert to his "now, on Earth" being December 2015. He always has to be seeing light from December 2014 because he hasn't moved much, and that's the light that's reached him.

What's going on?

If the alien simply accelerated instantaneously to 0.99c, came to Earth, and carried on by without stopping, how would we describe this on Earth? We'd say the alien was at rest 1ly away, accelerated to 0.99c, traveled for a fraction over a year, then zipped past us. While he was travelling, he was time-dilated and his clocks don't show a year to have passed, they show around 51 days for the approach to Earth.

But what about the alien? How can he travel one light year in fifty days? He can't - but that's fine because, for the alien, the distance to the Earth is length contracted to about fifty one light days. His clocks are ticking normally, and (from this perspective) the Earth is rushing towards him at 0.99c. In this perspective Earth is going to get to him in fifty one days. It must be about October 2016 "now" on Earth for him to arrive in December 2016...

 

[Nantes]

It must be about October 2016 "now" on Earth for him to arrive in December 2016...

October 2016 in whose perspective? If it's ours, he takes more than a year to arrive, so by all rights he can only arrive AFTER December 2016 (since it's December 2015 now), no?

This dang's confusing²³

 

[Herman Trivilino]

Is it because he's now in a transversal slice of the space time loaf of bread like Greene's video shows, and at his current point the present time is still the same, but the future-seeing effect is magnified through the distance from Earth?

At the faster speed the angle of the slice is greater. So events further in our future are simultaneous with events in his present. But this is not a future "seeing" because he won't see it until after it has happened to us.

 

[Ibix]

October 2016 in whose perspective? If it's ours, he takes more than a year to arrive, so by all rights he can only arrive AFTER December 2016 (since it's December 2015 now), no?

From the perspective of people on Earth, the alien started from one light year away in December 2015. He can't get here before December 2016 without breaking the speed of light.

From the perspective of the moving alien, it was already October 2016 when he set off and he arrives in December 2016.

 

[Nantes]

Oh my god, it makes perfect sense! This is the best moment since I started this thread! THANK YOU guys! Just to confirm I got it:

From the perspective of the moving alien, it was already October 2016

Because he inferred it based on his knowledge, not because there was anything physical that showed him that, right? Since he was at rest previously, his calendar was marking December 2015, same as us, before he started moving. But the instant he started moving towards Earth at 0.99c he knew (only because he's a PhD in Relativity) to adjust his calendar to October 2016, only so it would make internal sense for him (otherwise he'd advance 1 year in 51 days)... not because he was actually in October 2016 now. Is that it?

 

[Ibix]

Bingo.

 

[Nantes]

Bingo.

Damn, I don't ever want to own an extremely fast spacecraft , then. If I'm already annoyed with having to adjust my clock for daylight savings twice a year, imagine adjusting my calendar every time I stop and go!

 

[jartsa]

It must be about October 2016 "now" on Earth for him to arrive in December 2016...

Yes, but the alien can't calculate the arrival date, unless he knows the now date.

But luckily alien can calculate the now date without any knowledge of the future: He looks at an Earth calendar with a telescope, and adds the travel time of the light to that date.(Acceleration does not effect the date seen in the telescope's ocular, so if anything changes, it must be the travel time of the light that is seen by the alien peeking through the telescope)

 

[jartsa]

I'm intrigued by the whole thing about the alien moving towards Earth being able to see slices of the future. It would mean the future is already predetermined!

Let' say on year 2015 on Earth you observe what the Earth looks like at that time. Then you travel far away from earth, and then you accelerate away from earth, which causes the year on Earth according to you to become the year 1000.

Now you know something that the people on Earth on year 1000 don't know: How the Earth will be like on the year 2015.

What do you see in a telescope aimed on the earth? You may see for example the Earth on the year 3000. So yes, knowing the future is possible, and it's also quite pointless as you can also see the future whenever you know the future.

I guess the future of the Earth was predetermined as you found out that light from events existed before the events.

 

[Herman Trivilino]

What do you see in a telescope aimed on the earth? You may see for example the Earth on the year 3000.

Never and nowhere could you see light that left Earth in the year 3000 because it hasn't left yet.

So yes, knowing the future is possible, and it's also quite pointless as you can also see the future whenever you know the future.

No, no, and vacuous because you never know the future.

I guess the future of the Earth was predetermined as you found out that light from events existed before the events.

No, and no.

 

[jartsa]

Never and nowhere could you see light that left Earth in the year 3000 because it hasn't left yet.
No, no, and vacuous because you never know the future.
No, and no.

Do you perhaps mean that I made an error?

You are floating in space viewing the Earth through a telescope, seeing events from year 3000. Then you accelerate so that "now" on Earth becomes year 1000.

So it's year 1000 on Earth now, and you are seeing events from year 3000 happening.

 

[Nugatory]

Do you perhaps mean that I made an error?

You have.

You are floating in space viewing the Earth through a telescope, seeing events from year 3000. Then you accelerate so that "now" on Earth becomes year 1000.
So it's year 1000 on Earth now, and you are seeing events from year 3000 happening.

Try drawing a spacetime diagram of the situation you're describing. Can you find a timelike path that starts in the future light cone of the event "earth, year 3000" and ends on any possible line of simultaneity (spacelike straight line) through the event "earth, year 1000"?

 

[jartsa]

Try drawing a spacetime diagram of the situation you're describing. Can you find a timelike path that starts in the future light cone of the event "earth, year 3000" and ends on any possible line of simultaneity (spacelike straight line) through the event "earth, year 1000"?

The "earth year 3000" went to the future when "earth year 1000" became the current earth. But light from "earth year 3000" did not go to the future, because that light was not located near "earth year 3000".

The light source disappeared while the light from the light source remained, so clearly causality went out of the window. In block universe we don't need such thing as causality.

I'm interested to know why this is wrong. Maybe clocks never run backwards, no matter how you accelerate, because it seems like causality will suffer anytime clocks run backwards?

 

[Ibix]

Jartsa - "now on Earth" can never be earlier than the date you are seeing through your telescope. If it could, what you call now would be before something that you can see has already happened. You can see this from a space-time diagram, as Nugatory suggested, or from the Lorentz transforms - place the Earth at x=d in its rest frame, then insist that t'=0 and see what range of t you can get.

 

[DrGreg]

You are floating in space viewing the Earth through a telescope, seeing events from year 3000.

Let's suppose you are 100 light years from Earth (according to Earth) when this happens. Then, someone on Earth in the year 3100 would say your observation is occurring "now". (Because, according to Earth it takes 100 years for the light to travel 100 light-years.)

Then you accelerate so that "now" on Earth becomes year 1000.

That's not possible. Depending on your speed relative to Earth, the event on Earth that you describe as "now" must lie somewhere between 3000 and 3200 (3100±100) Earth time.

 

[Nugatory]

Try drawing a spacetime diagram...

The "earth year 3000" went to the future when "earth year 1000" became the current earth. But light from "earth year 3000" did not go to the future, because that light was not located near "earth year 3000".

Try drawing a spacetime diagram.

 

[jartsa]

I see. When I'm trying to reverse a distant clock, by a sharp acceleration of myself, the clock starts to resist further reversing at some time. Or rather: the more a clock is reversed, the more it resist reversing. Thank you guys. It's clear now.

Hmm ... If I make sharp motions back and forth, a distant clock advances a lot.

 

[Ibix]

I see. When I'm trying to reverse a distant clock, by a sharp acceleration of myself, the clock starts to resist further reversing at some time. Or rather: the more a clock is reversed, the more it resist reversing. Thank you guys. It's clear now.

Hmm ... If I make sharp motions back and forth, a distant clock advances a lot.

No - nothing happens to the clock. The only thing changing is your definition of "now" in the sentence "the time clocks on Earth are showing now is..." The point is that there are limits to what one can reasonably call "now". A time you can see, or have already seen, isn't sensible since you would be in the position of seeing things that happen after what you call now.

 

[Herman Trivilino]

I see. When I'm trying to reverse a distant clock, by a sharp acceleration of myself, the clock starts to resist further reversing at some time. Or rather: the more a clock is reversed, the more it resist reversing. Thank you guys. It's clear now.

Hmm ... If I make sharp motions back and forth, a distant clock advances a lot.

Making this kind of a thing "clear" is very difficult, as it's so far from what we experience.

You will make progress, I believe, by trying to understand that proper time is a relativistic invariant. For example, the clock you talk about keeps proper time as does your wristwatch. Just as the treading on your wrist watch will never jump or reverse, neither will that clock's reading. That's a relativistic invariant, meaning all observers will agree on that behavior.

When we talk about time dilation and relative simultaneity, we talk about what observers in motion relative to those clocks will observe when they compare them to the clocks they carry with them.