# Was I born before or after my older sister?

#### foobar

quote from wikipedia:
"According to the special theory of relativity, it is impossible to say in an absolute sense whether two distinct events occur at the same time if those events are separated in space, such as a car crash in London and another in New York. The question of whether the events are simultaneous is relative: in some reference frames the two accidents may happen at the same time, in other frames (in a different state of motion relative to the events) the crash in London may occur first, and in still other frames the New York crash may occur first. However, if the two events could be causally connected ("event A causes event B"), the causal order is preserved (i.e., "event A precedes event B") in all frames of reference"

My sister is 2 years older than me and not born in the same place.
Is there a frame where we are born at the same time ?
my fiddling with lorentz transformations seems to say yes. But I must be wrong.

How does the "causally connected" proviso prevent this?

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#### vanhees71

Gold Member
The difference of the four-vectors of the two events "sister born" and "you are born" is clearly timelike, and thus there's no question in which order both of you were born. As soon as you express a situation in a proper, i.e., covariant way, the apparanted paradoxes of relativity vanish and you can think about the really interesting physical problems instead of bothering yourself with the apparently "weird" consequences of the relativistic space-time structure. I don't know, why relativity seems to be still taught as if Minkowski never had written his famous paper on the mathematical structure of special relativity and why one emphasizes the apparent paradoxes rather than formulating relativistic physics in a covariant way, where such paradoxes never appear in the first place!

#### ghwellsjr

Gold Member
quote from wikipedia:
"According to the special theory of relativity, it is impossible to say in an absolute sense whether two distinct events occur at the same time if those events are separated in space, such as a car crash in London and another in New York. The question of whether the events are simultaneous is relative: in some reference frames the two accidents may happen at the same time, in other frames (in a different state of motion relative to the events) the crash in London may occur first, and in still other frames the New York crash may occur first. However, if the two events could be causally connected ("event A causes event B"), the causal order is preserved (i.e., "event A precedes event B") in all frames of reference"

My sister is 2 years older than me and not born in the same place.
Is there a frame where we are born at the same time ?
No.

my fiddling with lorentz transformations seems to say yes. But I must be wrong.

How does the "causally connected" proviso prevent this?
Your mother's sequence of events, no matter how she traveled between your sister's birthplace and yours, will maintain the same order in all frames of reference. Pairs of events can be closer together or farther apart in time in different frames but can never reach a zero time interval which is what would have to happen for the two of you to be born at the same time.

#### andromeda

quote from wikipedia:
"According to the special theory of relativity, it is impossible to say in an absolute sense whether two distinct events occur at the same time if those events are separated in space,
It does not seem right from any point of view. When we label time in the moving system as t' then according to official interpretation if t'=5 units then for any clock located anywhere events happening at clock time t'=5 will be called simultaneous.

Einstein in his 1905 ground breaking paper said:
We have so far defined only an “A time” and a “B time.” We have not defined a common “time” for A and B, for the latter cannot be defined at all unless we establish by definition that the “time” required by light to travel from A to B equals the “time” it requires to travel from B to A.,
Then he shows how to synchronise clocks. After this procedure a single value of clock indication is applicable everywhere (in theory as it would be hard to synchronise clocks 13 bln light years away)

Despite this, Einstein also said in his Autobiographical Notes written in 1945: “there is no such thing as simultaneity of distant events" which is what you have just said and it is difficult to reconcile with the previous statement.

#### foobar

sister birth event xs,ts. brother birth event xb, tb

ts+D=tb sister is D units older.

In some primed frame:

t's=γ(ts-vxs/c2)

t'b=γ(tb-vxb/c2)

t'b-t's=γ(D-v/c2(xb-xs))
=0 for simultaneous birth in primed frame.
so
xb-xs=Dc2/v

or v=Dc2/(xb-xs)

=c * c/(xb-xs)/D
=c * c/V
where mother moves at speed V from xs to xb. V would have to be faster than light to make v < c. So not possible. I think.

So is the wikepedia statement above about the crashes wrong, ie in some frame new York crash is first, in some it is not ?

#### Meir Achuz

Homework Helper
Gold Member
foobar: I hope you have learned not to rely on Wikipedia.

#### Fredrik

Staff Emeritus
Gold Member
So is the wikepedia statement above about the crashes wrong, ie in some frame new York crash is first, in some it is not ?
If you quoted it correctly, it's wrong. But if you replace "separated in space" with "spacelike separated", the statement will be correct.

The distance between New York and London is roughly 5500 km. So it takes light roughly 5500/300000 ≈ 0.018 seconds to travel that distance. If the two car crashes are less than that time apart according to clocks on Earth, then there's an inertial coordinate system in which they occur in the opposite order.

Hm, the figure of 5500 km is probably along the surface of the Earth. The distance along the shortest path is probably a bit less (I haven't thought about how much less), so 0.018 seconds is probably an overestimate.

#### russ_watters

Mentor
....so what is actually wrong with the wiki here? Just a minor wording issue? The OP tries to apply the scenario in reverse and does it wrong, but that's a flaw in the OP's scenario, not a flaw in the article's scenario.

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#### Andrew Mason

Homework Helper
....so what is actually wrong with the wiki here? Just a minor wording issue? The OP tries to apply the scenario in reverse and does it wrong, but that's a flaw in the OP's scenario, not a flaw in the article's scenario.
The Wikipedia article states:

"According to the special theory of relativity, it is impossible to say in an absolute sense whether two distinct events occur at the same time if those events are separated in space, such as a car crash in London and another in New York."

The problem is that it is possible to say whether the two events occur at the same time if, as Fredrik points out, the separation in distance divided by the separation in time in the earth frame of reference < c. In that case you can say that they are NOT simultaneous (ie. in any frame).

AM

#### russ_watters

Mentor
The Wikipedia article states:

"According to the special theory of relativity, it is impossible to say in an absolute sense whether two distinct events occur at the same time if those events are separated in space, such as a car crash in London and another in New York."

The problem is that it is possible to say whether the two events occur at the same time if, as Fredrik points out, the separation in distance divided by the separation in time in the earth frame of reference < c. In that case you can say that they are NOT simultaneous (ie. in any frame).

AM
So if we changed the word "whether" to "that", it'll be fine, right?

Honestly, that's how I read it anyway and the OP's scenario was much different: events that according to the clock did NOT happen at the same time.

In other words, the wiki is talking about events who's clocks show them to be happening at the same time(at least as a best case), but saying they aren't necessarily simultaneous, while the OP seems to be asking if events with clocks showing DIFFERENT times CAN be simultaneous.

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#### Andrew Mason

Homework Helper
So if we changed the word "whether" to "that", it'll be fine, right?

Honestly, that's how I read it anyway and the OP's scenario was much different: events that according to the clock did NOT happen at the same time.

In other words, the wiki is talking about events who's clocks show them to be happening at the same time(at least as a best case), but saying they aren't necessarily simultaneous, while the OP seems to be asking if events with clocks showing DIFFERENT times CAN be simultaneous.
If the Wikipedia article simply stated that events (A and B) that are spatially separated and simultaneous as measured in one frame of reference are not simultaneous in other inertial reference frames, it would be fine.

In all other inertial reference frames that are in relative motion in the direction of the displacement vector between the event locations, the events would not be simultaneous. In some, event A would occur before B and in others B would occur before A.

AM

#### foobar

This in particular Im wondering about. Can the London crash occur first in some frame, and the new York crash be first in some other frame? :
" in other frames (in a different state of motion relative to the events) the crash in London may occur first, and in still other frames the New York crash may occur first."

#### Matterwave

Gold Member
This in particular Im wondering about. Can the London crash occur first in some frame, and the new York crash be first in some other frame? :
" in other frames (in a different state of motion relative to the events) the crash in London may occur first, and in still other frames the New York crash may occur first."
Only if the two events are space-like separated. As Fredrik calculated, this means the time between the events as measured from the Earth's frame of reference has to be <.018s (upper bound).

If, according to an observer on Earth, the New York crash happened at t=0, and the London crash happened at t>.018s, then ALL observers will see the New York crash happen first.

#### Fredrik

Staff Emeritus
Gold Member
This in particular Im wondering about. Can the London crash occur first in some frame, and the new York crash be first in some other frame?
Yes, if they occur simultaneously (or at least approximately less than 0.018 seconds apart) according to clocks at rest on Earth, this is exactly what happens. If the two crashes were (say) 1 second apart, all inertial coordinate systems will agree about which crash happened first.

When I said that the statement you quoted was wrong, I didn't consider the possibility that the next few words after "if those events are separated in space," were something like "but not in time". If it continued with something like that, the full statement is fine.

OK thats clear.

#### ghwellsjr

Gold Member
My sister is 2 years older than me and not born in the same place.
Is there a frame where we are born at the same time ?

Your issue is, why can't we transform this scenario to one where the red dot at the beginning of your mother's blue worldline and the black dot at the end are at the same Coordinate Time:
How does the "causally connected" proviso prevent this?
Your mother's blue worldline is a series of "causally connected" events (dots) representing one month increments of Proper Time for your mother. They will always remain connected in the same order in all other frames although the spacing between the dots can vary but they will never be closer than one month of Coordinate Time.

Let's start by transforming to the rest frame of your mother while she is traveling away from your sister:

Notice that your mother's time in this frame is going faster during the first part of her trip compared to the previous frame and slower during the second part of her trip compared to the previous frame. This is an example of what I said in post #3:
Pairs of events can be closer together or farther apart in time in different frames but can never reach a zero time interval which is what would have to happen for the two of you to be born at the same time.
Another issue that you raised in this thread is the order that pairs of events can occur in according to different frames. Note that in this frame your mother turns around before your sister reaches 11 months whereas in her rest frame, those two events are simultaneous. Also note in this frame that your sister reaches her second birthday (24 months) before you are born. Finally note that the times on your mother's and your sister's clocks are the same in this frame as they were in the first frame when your mother passes your sister on her way back. That's because it is a single event where they are colocated.

Now let's transform to the frame in which your mother is at rest during the return part of her trip:

This time your sister reaches 11 months before your mother turns around and your sister has her second birthday after you are born but both your sister and your mother are again the same ages when they pass as they were in the two previous frames.

Now to stress the point that no frame will allow both of you to be born at the same time, we first transform to a frame at 99%c:

As you can see, all the events and all the worldlines approach the 45-degree diagonal that represents the speed of light and the Coordinate Time difference between your sister's birth and your birth has gotten quite large going from 24 months to almost 185 months. If we transformed to an even higher speed, we would get even closer to the 45-degree diagonal but the Coordinate Time difference would be even larger so there's no hope increasing the speed of the transformed frame.

What happens if we go the other way to -99%c?

The events all go the other way but still approach the 45-degree diagonal on the other side. It's only slightly different with the Coordinate Time difference between your birth times being just over 155 months.

Well is there any way to decrease the Coordinate Time difference between your birth times below 24 months? Actually there is. If we transform to a speed of -10%c we get:

This is barely an improvement but it's the best we can do with this scenario.

Well, I hope these diagrams help. If you need any more help understanding them, please ask.

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#### foobar

ghwellsjr
very impressive analysis, only spotted it later. thanks

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