Relativity of simultaneity; Causality; Andromeda Paradox

take everything

Hi lads.
I'm not a physicist, just someone who finds some physics fascinating.
I was wondering the other day about what relativity of simultaneity really meant and about its implications.
Specifically i was wondering how consistent it was with causality for example.

I started to wonder what events (and their sequencing) on earth would look like if you whizzed around at close to the speed of light back and forth.
I know that moving at this speed significantly changes your present compared with someone who is stationary. So the first thing i wondered was is there any way the sequence of events on earth could get jumbled for you when you travelled at this speed.
I thought probably not.

But then i started looking into this a bit more and i came across stuff like the Andromeda Paradox.
If i understand this correctly, it's a thought experiment where two people pass each other on earth while both observe the Andromeda galaxy. Each of them have their own separate "plane of simultaneity" (meaning their presents are different) so one of them observes an Andromeda space fleet setting off on a journey and the other is still uncertain whether the fleet has taken off yet.

Basically can relativity of simultaneity in any way screw up causality. Or is the fact that information transmission is necessarily subluminal what preserves all this.

I'm struggling a bit with this.
So i just wanted to get some proper ideas on it.
Thanks.

Edit: I've edited my post because i've just realised i've misinterpreted the Andromeda paradox.
Need to read more about this.
Sorry

Morbert

take everything wrote: »

Hi lads.
I'm not a physicist, just someone who finds some physics fascinating.
I was wondering the other day about what relativity of simultaneity really meant and about its implications.
Specifically i was wondering how consistent it was with causality for example.

I started to wonder what events (and their sequencing) on earth would look like if you whizzed around at close to the speed of light back and forth.
I know that moving at this speed significantly changes your present compared with someone who is stationary. So the first thing i wondered was is there any way the sequence of events on earth could get jumbled for you when you travelled at this speed.
I thought probably not.

Causality is preserved in relativity. This means that, while people might disagree with the simultaneity of events, they will agree with which events caused, and hence preceded other events.

But then i started looking into this a bit more and i came across stuff like the Andromeda Paradox.
If i understand this correctly, it's a thought experiment where two people pass each other on earth while both observe the Andromeda galaxy. Each of them have their own separate "plane of simultaneity" (meaning their presents are different) so one of them observes an Andromeda space fleet setting off on a journey and the other is still uncertain whether the fleet has taken off yet.

This seems to suggest that there may be a way of letting the person who hasn't sen the fleet taken off yet that it has (letting them see the future as it were).

Information propagates at a finite speed. This means that, even though the fleet has taken off in one observer's present, that observer does not know whether or not the fleet has taken off yet. Causality can't be violated.

There's another thought experiment involving a spacecraft travelling at near-light speed that fires lasers from both ends of the craft so they meet in the middle, and in so doing set of a mechanism that kills a cat.
However, a stationary observer observing this spacecraft will not see the two lasers meet in the middle and so in his frame of reference the cat will not be killed.

These are just a couple of things that have me scratching my head about the implications of the relativity of simultaneity.
Basically can relativity of simultaneity in any way screw up causality. Or is the fact that information transmission is necessarily subluminal what preserves all this.

I'm struggling a bit with this.
So i just wanted to get some proper ideas on it.
Thanks.

Co-incident events (events that happen at the same place and time) are also preserved under relativity. This means if one observer sees two lasers simultaneously strike and activate a mechanism, all observers will. In the above case, both observers agree that both lasers simultaneously strike the mechanism, but they will disagree over when each laser was fired from the ship. One will say both were fired simultaneously. The other will say one was fired before the other.

take everything

Causality is preserved in relativity. This means that, while people might disagree with the simultaneity of events, they will agree with which events caused, and hence preceded other events.

OK thanks.
I thought this but is there a way of showing it (ie that all that messing around with past/present etc doesn't jumble around a cause event and an effect event). Is it kind of like all frames of reference are insulated from each other (that no information could be sent soon enough between them to lead to a violation of causality). Or something
Tell me if i'm talking ****e. :pac:

Information propagates at a finite speed. This means that, even though the fleet has taken off in one observer's present, that observer does not know whether or not the fleet has taken off yet. Causality can't be violated.

This is my main query. If the two people are passing each other, couldn't person A who sees the event happening pass a message on to person B to say it's happening (before person B eventually sees it himself). OK this isn't necessarily a violation of causality. But something funky would be happening. Person B would now "know" the future via person A's message.
Can this happen.
And if so, is it a big deal (in terms of causality).

Thanks.

Morbert

take everything wrote: »

OK thanks.
I thought this but is there a way of showing it (ie that all that messing around with past/present etc doesn't jumble around a cause event and an effect event). Is it kind of like all frames of reference are insulated from each other (that no information could be sent soon enough between them to lead to a violation of causality). Or something
Tell me if i'm talking ****e. :pac:

Consider two events A and B in a reference frame S. The time between these two events Δt is positive (I.e. B happened after A) and A and B are causally related (i.e. Δx/Δt < c) (Δx is the distance between events). The question we have to ask is if there is a reference frame S' such that B happened before A (Δt' is negative). The relevant lorentz transformation is

Δt' = ɣ(Δt - Δx v/c^2)

The question is therefore: For which values of v is ɣ(Δt - Δx v/c^2) < 0. A little rearranging:

ɣ(Δt - Δx v/c^2) < 0
Δt - Δx v/c^2 < 0
Δx v/c^2 > Δt
v > Δt/Δx c^2

We know that the events are causally related, so Δt/Δx > 1/c

v > (1/c) c^2
v > c

So in order for the order of events to be reversed, the speed of S' with respect to S would have to be greater than the speed of light, c. Under relativity, this is impossible for any observer, (whether they are a human being, or a particle of light)! Hence, causality is preserved for all observers subject to the laws of physics.

This is my main query. If the two people are passing each other, couldn't person A who sees the event happening pass a message on to person B to say it's happening (before person B eventually sees it himself). OK this isn't necessarily a violation of causality. But something funky would be happening. Person B would now "know" the future via person A's message.
Can this happen.
And if so, is it a big deal (in terms of causality).

Thanks.

By the time the signal from Andromeda reaches A, they will be too far from B to send any message "ahead" of time. It would violate causality if they could. You could set up a series of relays such that B was affected by an event in andromeda before the event occured. It would also mean that, in the reference frame of B, person A was affected by an event in Andromeda before the event occured. Such a scenario can't be realised under the lorentz transformations, as shown in the first part of my response.

RichieC

I just want to put rhis out here see if Im missing something.

Time dialation occurs due to our speed traveling through space. This I take it includes the speed we move on earth plus the speed of our planet plus our sun and the speed of our galaxies movement through inter galactic space? (correct me if im wrong here)

now, assuming all galaxies arent moving about at the same speed would I be right in assuming time is different in each galaxy?

A documentary called the fabric of space tried to explain I think this but im not sure i gathered it correctly.

Morbert

RichieC wrote: »

I just want to put rhis out here see if Im missing something.

Time dialation occurs due to our speed traveling through space. This I take it includes the speed we move on earth plus the speed of our planet plus our sun and the speed of our galaxies movement through inter galactic space? (correct me if im wrong here)

Close. Time dilation is the change in "passage" of time of objects who are in motion with respect to one another. There is no absolute background space serving as a standard of "proper" time. So we can't say a galaxy is absolutely moving. We can only say it is moving with respect to another galaxy.

now, assuming all galaxies arent moving about at the same speed would I be right in assuming time is different in each galaxy?

A documentary called the fabric of space tried to explain I think this but im not sure i gathered it correctly.

Yes. You don't even need to go as far as other galaxies. We have detected a difference in time on planes as they fly around earth. Time is different for GPS satellites as well, which is why GPS technology needed relativity to make corrections.