B An issue about the twin paradox

[dwspacetime]

TL;DR Summary

How can the twin meet again at the same time?

For two people to meet in space-time we have to agree on location and time. For instance two have to make an appointment like this, I meet you at this address at 5pm tomorrow. All 4 coordinates have to match. If the traveling twin experiences less time, when the two finally meet again, they have to make appointment at the same location but not the same time. How could that happen?

 

[Orodruin]

TL;DR Summary: How can the twin meet again at the same time?

For two people to meet in space-time we have to agree on location and time. For instance two have to make an appointment like this, I meet you at this address at 5pm tomorrow. All 4 coordinates have to match. If the traveling twin experiences less time, when the two finally meet again, they have to make appointment at the same location but not the same time. How could that happen?

You are confusing coordinate time with proper time. Coordinates specify events, proper time measures the time passed for an observer.

 

[hutchphd]

Suppose instead that the traveler drove to Chicago for the overnight and returned in the morning to meet me for lunch at the restaurant down the block. How could we meet? He has traveled (experienced a distance of) several hundred miles since last we met and I have travelled (experienced a distance of) half a block!!!!!And yet here we are. How can this possibly be???
Does this help highlight the flaw in your incredulity?

/

 

[FactChecker]

For two people to meet in space-time we have to agree on location and time.

They can meet, regardless if their spacetime coordinates agree. If my watch is slow, or even stopped, I can still meet people on the street. Those events happen, regardless of how different people record them in their spacetime coordinates.

 

[Nugatory]

How could that happen?

They've agreed to meet wherever the earth is, and they don't need to agree about the time because earth twin is going to be there waiting all along. It's as if you and I are hanging out in Trafalgar square, I say that I'm going off sightseeing, you say "OK, I'll stay here, meet back here when you're done".

More complicated situations are handled by specifying the rendezvous using mutually agreed coordinates. We're in London, you're going to spend a few days in New York and I'm going to Paris, we agree "back at our London apartment at 6:00 in the evening Saturday". It doesn't matter that Paris and New York are in different times and we'll adjust our watches accordingly, as long as we've agreed that we mean 6:00 PM London time and we know how to convert between London, Paris, and New York time.
In your example,,, the twins' watches doesn't track each other's time, but we do know how to calculate the difference and that all it takes to arrange the rendezvous.

 

[Dale]

TL;DR Summary: How can the twin meet again at the same time?

If the traveling twin experiences less time, when the two finally meet again, they have to make appointment at the same location but not the same time

Geometrically, this is like saying that you can’t have a semicircle intersect a diameter at two points because the semicircle is longer than the diameter.

 

[dwspacetime]

Suppose instead that the traveler drove to Chicago for the overnight and returned in the morning to meet me for lunch at the restaurant down the block. How could we meet? He has traveled (experienced a distance of) several hundred miles since last we met and I have travelled (experienced a distance of) half a block!!!!!And yet here we are. How can this possibly be???
Does this help highlight the flaw in your incredulity?

/

This doesn't explain anything. Just like in a 3d world we need 3 coordinates to pin point an exact point, in a 4d world we need to 4 coordinates to do the samething. You will not meet your friend if you are in new York but I'm in Chicago even two of the three coordinates but one match. You will not meet another even three of coordinates but one match in our 4 d world. If you do meet each other without the time coordinate match I need an explanation. If you do meet another person in new York when you are in Chicago tell me how you do it.

 

[dwspacetime]

They've agreed to meet wherever the earth is, and they don't need to agree about the time because earth twin is going to be there waiting all along. It's as if you and I are hanging out in Trafalgar square, I say that I'm going off sightseeing, you say "OK, I'll stay here, meet back here when you're done".

More complicated situations are handled by specifying the rendezvous using mutually agreed coordinates. We're in London, you're going to spend a few days in New York and I'm going to Paris, we agree "back at our London apartment at 6:00 in the evening Saturday". It doesn't matter that Paris and New York are in different times and we'll adjust our watches accordingly, as long as we've agreed that we mean 6:00 PM London time and we know how to convert between London, Paris, and New York time.
In your example,,, the twins' watches doesn't track each other's time, but we do know how to calculate the difference and that all it takes to arrange the rendezvous.

In space-time we need 4 coordinates to determine an exact location. If time for the twin are not the same they just can't be at the exact spot in space-time.

 

[Nugatory]

Just like in a 3d world we need 3 coordinates to pin point an exact point, in a 4d world we need to 4 coordinates to do the samething.

Sure, but there’s no reason why the time coordinate used to identify the moment of the rendezvous must be related to the proper time either one experiences.

 

[Nugatory]

In space-time we need 4 coordinates to determine an exact location. If time for the twin are not the same they just can't be at the exact spot in space-time.

Certainly they can. Two different four-tuples of coordinate values can label the same point in spacetime, just as two different three-tuples of spatial coordinates can label the same point in space.

 

[Dale]

In space-time we need 4 coordinates to determine an exact location. If time for the twin are not the same they just can't be at the exact spot in space-time.

Coordinates and events are different things. Just like a map and the territory are different things. We can use different maps to refer to the same place.

 

[Herman Trivilino]

In space-time we need 4 coordinates to determine an exact location. If time for the twin are not the same they just can't be at the exact spot in space-time.

In the twin paradox it's assumed that the staying twin will stay in the same place, so all the traveling twin need do is agree to return to that place, and it's guaranteed they'll meet up.

 

[DaveC426913]

This doesn't explain anything. Just like in a 3d world we need 3 coordinates to pin point an exact point, in a 4d world we need to 4 coordinates to do the samething. You will not meet your friend if you are in new York but I'm in Chicago even two of the three coordinates but one match.

As others have tried to point out: the meeting point in space doesn't have to be a mystery. For starters, don't tell your friend to go to Chicago if you are in New York!

You will not meet another even three of coordinates but one match in our 4 d world. If you do meet each other without the time coordinate match I need an explanation

Stay-at-home twin to travelling twin: "When you're on your way back, be sure to come back to Earth - wherever it is. Then come back to our apartment. I will be here, waiting."

Space coordinates match: check!
Time coordinate match: check!

. If you do meet another person in new York when you are in Chicago tell me how you do it.

So don't do that!

Note that the probem you are imagining is generic - it has nothing to do with relativity.

Even here on Earth, in your neighborhood at walking speed, if you agree on a place (the coffee shop) but your friend doesn't know when he'll be done his interview, you can always just go there and wait.

Since we know how to avoid this problem when we go for coffee, there's no reason we can't use the same method for a space journey.

 

[PeterDonis]

In space-time we need 4 coordinates to determine an exact location.

Yes.

If time for the twin are not the same they just can't be at the exact spot in space-time.

No. Proper time is not a coordinate. The twins aren't agreeing to meet back on Earth when both of their watches read the same time. They are agreeing to meet back on Earth when, for example, the big clock in the clock tower above the Earth twin's apartment reads a particular time. That's a coordinate time, not either twin's proper time. (If the Earth twin has remained at rest with respect to the tower during the whole scenario, then the clock tower coordinate time will match the Earth twin's proper time--but that's not necessary for the scenario to work.)

Or, as others have posted, the twins could just not specify a particular time to meet again at all--they could just say that the traveling twin will return to the Earth twin's location whenever he gets there, and the Earth twin will wait there the whole time. In either case, the supposed problem you are claming is there simply does not exist.

 

[Dale]

If time for the twin are not the same they just can't be at the exact spot in space-time.

You are misunderstanding the geometry of spacetime. The age of the twins is a length in spacetime, not a coordinate. Two paths can meet even if they don’t have the same length

 

[PeroK]

In space-time we need 4 coordinates to determine an exact location. If time for the twin are not the same they just can't be at the exact spot in space-time.

Hafele and Keating proved this is false. Atomic clocks went out of sync after taking different journeys on commercial airlines:

https://en.wikipedia.org/wiki/Hafele–Keating_experiment

 

[Ibix]

For two people to meet in space-time we have to agree on location and time. For instance two have to make an appointment like this, I meet you at this address at 5pm tomorrow. All 4 coordinates have to match. If the traveling twin experiences less time, when the two finally meet again, they have to make appointment at the same location but not the same time. How could that happen?

You would need to agree whose watch you were using to define 5pm - much as you have to do if you call family in another timezone. All relativity adds to this is new ways for watches to be out of sync, apart from deliberate or accidental mis-setting.

At a more fundamental level, it turns out that your watch measures the "distance" you travel through spacetime. In space there is more than one route through space between two chosen points, and the routes don't necessarily have the same length. In spacetime there is more than one route between two events and the routes don't necessarily have the same "length", so you don't necessarily experience the same time between them.

It's also worth noting, if it wasn't obvious, that "time" is a word that covers multiple different concepts in relativity. One is coordinate time, which is a kind of agreed system of clocks that we define to be at rest. The other is proper time, which is what each individual's wristwatch (or hypothetical wristwatch if we are talking about a particle or something) shows, which will not generally agree. The same concepts are available in pre-relativistic physics, but it's a distinction without a difference there. However, if you confuse the two in relativity (which is what I suspect you're doing) you end up in a contradictory mess.

 

[sophiecentaur]

Hafele and Keating proved this is false. Atomic clocks went out of sync after taking different journeys on commercial airlines:

https://en.wikipedia.org/wiki/Hafele–Keating_experiment

In order to 'meet' after an interplanetary trip, both twins will need to know what 'time offset' the other will be experiencing so they can calculate where and when the meeting can happen. We have to ignore the necessary motion of the twin on a real orbiting / spinning Earth.

 

[Orodruin]

In order to 'meet' after an interplanetary trip, both twins will need to know what 'time offset' the other will be experiencing so they can calculate where and when the meeting can happen. We have to ignore the necessary motion of the twin on a real orbiting / spinning Earth.

They do not. It is sufficient that the staying twin specifies "I will be waiting right here". If the travelling twin just makes sure to get to that place, they will meet again since all that is required is that the world lines intersect, not where they intersect.

 

[Dale]

if you confuse the two in relativity (which is what I suspect you're doing)

I think so too. It is the same issue that you get geometrically if you confuse coordinates with length.

 

[sophiecentaur]

In order to 'meet' after an interplanetary trip, both twins will need to know what 'time offset' the other will be experiencing so they can calculate where and when the meeting can happen. We have to ignore the necessary motion of the twin on a real orbiting / spinning Earth.

If you take the thought experiment to interstellar proportions and to more practical conditions, there will be situations where the times cannot coincide because of the unavoidable time window which could be smaller than large time shifts. ("He died last year." or "It's spring so the Earth is the other side of the Sun right now", for instance.) I know that's not the basic theory but we all acknowledge the space issue and the space time issue can be there too.

 

[FactChecker]

There is a difference between the simple, physical, event of the twins meeting versus the complicated act of planning when and where to meet. For the twins to meet is simple physics. Agreeing on when and where the meeting takes place requires understanding the difference in coordinate systems. There is a lot the twins will disagree on if they do not understand special relativity.

 

[robphy]

TL;DR Summary: How can the twin meet again at the same time?

I meet you at this address at 5pm tomorrow. All 4 coordinates have to match.

You will not meet another even three of coordinates but one match in our 4 d world. If you do meet each other without the time coordinate match I need an explanation.

In space-time we need 4 coordinates to determine an exact location. If time for the twin are not the same they just can't be at the exact spot in space-time.

Yes, when two curves [worldlines] (call them a and b) meet,
"their coordinates must match" at the intersection point [event] (call it Z).
Elaborating on this:
"their coordinates must match [at Z]"
means that
"on a coordinate-chart, a point on curve-a and a point on curve-b have the same coordinates [as point Z]".
It doesn't matter which coordinate-chart, as long as it can describe point Z and the points on curve-a and on curve-b near point Z.

Said another way,
curve-a and curve-b meet [at Z] when,
"using curve-a coordinates, a point on curve-a and a point on curve-b have the same [a-]coordinates"
and
"using curve-b coordinates, a point on curve-a and a point on curve-b have the same [b-]coordinates".

"their coordinates must match [at Z]"
does not mean
"the coordinates of Z on a coordinate-chart associated with curve-a
must match
the coordinates of Z on a coordinate-chart associated with curve-b".

 

[ahmadphy]

In classical physics, a meeting occurs when two objects occupy the same position in space at the same time—something all observers agree on due to absolute space and time. In special relativity, simultaneity is relative, but if two objects share the same spacetime coordinates in one inertial frame, this event is invariant under Lorentz transformations. Therefore, the meeting is observed to occur in all inertial frames, even if the timing of events may differ between observers.

 

[Dale]

if two objects share the same spacetime coordinates in one inertial frame, this event is invariant under Lorentz transformations

Yes, and it is also invariant under all other coordinate transforms as well.