aradox
NB: This thread is placed here as the nature of the question is deamed too speculative to be placed in the physics and maths subforum, despite it is trying to obtain an answer in terms of mainstream science from the sciforum members
So I was thinking about the Grandfather paradox again after watching Primer and reading a bunch of time travel related articles (which I am still reading when this post was written)
I then thought about a possible model of time travel and tried to investigate on what happens
In order to take "decision" out of the equation (because it can complicate things), I simplify the grandfather paradox, which is commonly portrayed as "you go back in time and kill you grandfather" into
"There's a billard ball travelling inertially along the x direction with a velocity v<<c (so that special relativity effects become negligible) which then travel back in time (via CTC or Primer like reverse time) and on colliding with its past self, knock its past self off course so that it can no longer travel back (thus a grandfather paradox is created)"
because of how the minimal requirement of the grandfather paradox is that "An entity travels back in time to prevent its past from travelling in the first place"
Although I have read from an academic source on how physicists deal with grandfather paradox,
http://plato.stanford.edu/entries/time-travel-phys/
that by considering a spacetime with closed timelike curves (CTCs),
I am still wondering about what happen if a grandfather paradox occur in time travel models where the timeline is malleable (something like Back to The Future), known as type 3 time travelling models in scifi
From what I understand about time, there cannot be just one time axis as otherwise all overwrites will take place "at the same time" and you only get to see the latest revision of history of the timeline, thus I suspect time travel in these stories are at least 2 time dimensional (which I call them t and tau) and there units are seconds (s) and hyperseconds (hs) respectively. Points are notated as (t,tau). Thus t is time that we are familiar with, while tau is a continuum where the changes in the timeline is plotted (as if the entire timeline(t) is a 'block' of some sort and that tau records the changes that happens on this spacetime 'block' due to time travel)
[Assumptions]
Assume t and tau have the same ratio (i.e. 1s in t is the same as 1hs in tau)
Assume ripple effects can only propagate at maximum the speed c
So for any non time travellers that is travelling inertially with v<<c, its worldline will look like this (Fig 1)
For a time traveller entering a CTC, its worldline will look like this (Fig 2)
For a time traveller entering a Primer like time travelling box, its worldline will look like this (Fig 3)
So for a time traveller trying to initiate a grandfather paradox in a CTC, it will look like this (Fig 4a)
(From bottom left to top right)
(Frame of the time travelling ball that initiate the grandfather paradox)
1. There's a time travelling ball A that travel towards a wormhole to its left. (diagonal mint green line)
2. At (1,1), the ball have entered the wormhole and found itself in (0,1), which then knock its past self (A2) off course from the wormhole in a glancing elastic collision, thus creating a grandfather paradox
3. The ball A then continue to travel somewhere in the opposite direction (long diagonal mint green line that follows)
(Frame of A's copy (A2) at tau=1hs)
1. (0,1) A2 is knocked off course by A, history is changed in an inconsistent way and a ripple effect is generated
2. (1,2) Ripple effect propagates (pink line), there is no A2 that travel back to (0,2) to knock its past (A3) off course, thus A3 go into the wormhole like what A does and initiate the same series of events (pink diagonal and mint green vertical line at tau=3hs)
3. Meanwhile, A2 travel to a different direction thus it never entered the wormhole (long red diagonal line)
and so on...
For a time traveller trying to initiate a grandfather paradox via a Primer box, it will look like this (Fig 4b)
(From bottom left to top right, all vertical lines are projections on the t axis, as events happening on the t axis is what (we assume) an entity can perceive)
(Frame of the time travelling ball that initiate the grandfather paradox)
1. There's a time travelling ball A that travel towards a Primer box to its left. (diagonal mint green line)
2. At (1,1), the ball have entered the Primer box and found itself in (0,2), which then knock its past self (A2) off course from the wormhole in a glancing elastic collision, thus creating a grandfather paradox
3. The ball A then continue to travel somewhere in the opposite direction (long diagonal mint green line that follows)
(Frame of A's copy (A2) at tau=2hs)
1. (0,2) A2 is knocked off course by A, history is changed in an inconsistent way and a ripple effect is generated
2. (1,3) Ripple effect propagates (pink line), there is no A2 that travel back to (0,4) to knock its past (A3) off course, thus A3 go into the Primer box like what A does and initiate the same series of events (red diagonal and pink diagonal at tau=4hs)
3. Meanwhile, A2 travel to a different direction thus it never entered the Primer box (long red diagonal line)
and so on...
Observations:
1. Therefore to the time travelling ball and other observers, it seems the past of the time travelling ball alternates discontinuously between "time travelled ("grandfather lived" state) and "not time travelled" ("grandfather dead" state). As time (both t and tau) progress, this whole "dead" and "alive" states propagates as a whole like a wave with the source at t=0s
2. It seems the ripple effect will never catch up with A as it is always 1s (or 2s in the Primer box scenario) behind A. Thus it seems to suggest that a time traveller can do anything it wants and will not be erased from existence unless under special conditions
3. If A travels back in time again (e.g. via another wormhole or Primer box), then using these graphs it seems its worldline will intersect with the red line (the ripple effect). Thus it seems to suggest it will then be erased from existence since at the point of intersection, the ripple effect had caught up with the time traveller. A still exist before it is wiped out by the ripple effect since the ripple effect only took place at a certain tau
4. When the time interval between going from the past to present and then back to past to cause the gradnfather paradox tends to zero (i.e. length of the base of the triangles tend to zero), the oscillations in the timeline tends to infinity as it move to larger tau. Thus the opposite versions of histories (the "dead" and "alive" state) are only being separated by an infinitestimal amount
5. As seen by A and its hyper later copies as it look back to the past as it marches along tau, it seems what A can see in its immediate past is that everything proceed as the "alive" state with only at one instance of tau (tau=2hs in CTC scenario and tau=3hs in Primer box scenario) the history is in the "dead" state
Questions (numbered according to the observations):
1. This is weird, did I made a logical error in my deductions, or is it really what theoretically will happen given my assumptions stated above. Are discontinuities in events in time allowed?
2. This is even weird, is it really true that the ripple effect will never catch up?
3. Actually, how to interpret the physically meaning of the intersections?
4. This is pathological, how to deal with this infinite oscillating history?
5. This is also weird, did I made a mistake in my deduction?
6. Using mainstreams physics as we know it, is self consistent time travel the only solution? Is there exists any theories that can address the grandfather paradox without forbidding it to happen (other than Many Worlds Interpretaton, which some still thought it had not adequately address the paradox), or is there any concrete result that can rule out all possible types of grandfather paradoxes that can theoretically happen?
View attachment 6796
NB: This thread is placed here as the nature of the question is deamed too speculative to be placed in the physics and maths subforum, despite it is trying to obtain an answer in terms of mainstream science from the sciforum members
So I was thinking about the Grandfather paradox again after watching Primer and reading a bunch of time travel related articles (which I am still reading when this post was written)
I then thought about a possible model of time travel and tried to investigate on what happens
In order to take "decision" out of the equation (because it can complicate things), I simplify the grandfather paradox, which is commonly portrayed as "you go back in time and kill you grandfather" into
"There's a billard ball travelling inertially along the x direction with a velocity v<<c (so that special relativity effects become negligible) which then travel back in time (via CTC or Primer like reverse time) and on colliding with its past self, knock its past self off course so that it can no longer travel back (thus a grandfather paradox is created)"
because of how the minimal requirement of the grandfather paradox is that "An entity travels back in time to prevent its past from travelling in the first place"
Although I have read from an academic source on how physicists deal with grandfather paradox,
http://plato.stanford.edu/entries/time-travel-phys/
that by considering a spacetime with closed timelike curves (CTCs),
a box to contain some mainstream stuff said:
I am still wondering about what happen if a grandfather paradox occur in time travel models where the timeline is malleable (something like Back to The Future), known as type 3 time travelling models in scifi
From what I understand about time, there cannot be just one time axis as otherwise all overwrites will take place "at the same time" and you only get to see the latest revision of history of the timeline, thus I suspect time travel in these stories are at least 2 time dimensional (which I call them t and tau) and there units are seconds (s) and hyperseconds (hs) respectively. Points are notated as (t,tau). Thus t is time that we are familiar with, while tau is a continuum where the changes in the timeline is plotted (as if the entire timeline(t) is a 'block' of some sort and that tau records the changes that happens on this spacetime 'block' due to time travel)
[Assumptions]
Assume t and tau have the same ratio (i.e. 1s in t is the same as 1hs in tau)
Assume ripple effects can only propagate at maximum the speed c
So for any non time travellers that is travelling inertially with v<<c, its worldline will look like this (Fig 1)
For a time traveller entering a CTC, its worldline will look like this (Fig 2)
For a time traveller entering a Primer like time travelling box, its worldline will look like this (Fig 3)
So for a time traveller trying to initiate a grandfather paradox in a CTC, it will look like this (Fig 4a)
(From bottom left to top right)
(Frame of the time travelling ball that initiate the grandfather paradox)
1. There's a time travelling ball A that travel towards a wormhole to its left. (diagonal mint green line)
2. At (1,1), the ball have entered the wormhole and found itself in (0,1), which then knock its past self (A2) off course from the wormhole in a glancing elastic collision, thus creating a grandfather paradox
3. The ball A then continue to travel somewhere in the opposite direction (long diagonal mint green line that follows)
(Frame of A's copy (A2) at tau=1hs)
1. (0,1) A2 is knocked off course by A, history is changed in an inconsistent way and a ripple effect is generated
2. (1,2) Ripple effect propagates (pink line), there is no A2 that travel back to (0,2) to knock its past (A3) off course, thus A3 go into the wormhole like what A does and initiate the same series of events (pink diagonal and mint green vertical line at tau=3hs)
3. Meanwhile, A2 travel to a different direction thus it never entered the wormhole (long red diagonal line)
and so on...
For a time traveller trying to initiate a grandfather paradox via a Primer box, it will look like this (Fig 4b)
(From bottom left to top right, all vertical lines are projections on the t axis, as events happening on the t axis is what (we assume) an entity can perceive)
(Frame of the time travelling ball that initiate the grandfather paradox)
1. There's a time travelling ball A that travel towards a Primer box to its left. (diagonal mint green line)
2. At (1,1), the ball have entered the Primer box and found itself in (0,2), which then knock its past self (A2) off course from the wormhole in a glancing elastic collision, thus creating a grandfather paradox
3. The ball A then continue to travel somewhere in the opposite direction (long diagonal mint green line that follows)
(Frame of A's copy (A2) at tau=2hs)
1. (0,2) A2 is knocked off course by A, history is changed in an inconsistent way and a ripple effect is generated
2. (1,3) Ripple effect propagates (pink line), there is no A2 that travel back to (0,4) to knock its past (A3) off course, thus A3 go into the Primer box like what A does and initiate the same series of events (red diagonal and pink diagonal at tau=4hs)
3. Meanwhile, A2 travel to a different direction thus it never entered the Primer box (long red diagonal line)
and so on...
Observations:
1. Therefore to the time travelling ball and other observers, it seems the past of the time travelling ball alternates discontinuously between "time travelled ("grandfather lived" state) and "not time travelled" ("grandfather dead" state). As time (both t and tau) progress, this whole "dead" and "alive" states propagates as a whole like a wave with the source at t=0s
2. It seems the ripple effect will never catch up with A as it is always 1s (or 2s in the Primer box scenario) behind A. Thus it seems to suggest that a time traveller can do anything it wants and will not be erased from existence unless under special conditions
3. If A travels back in time again (e.g. via another wormhole or Primer box), then using these graphs it seems its worldline will intersect with the red line (the ripple effect). Thus it seems to suggest it will then be erased from existence since at the point of intersection, the ripple effect had caught up with the time traveller. A still exist before it is wiped out by the ripple effect since the ripple effect only took place at a certain tau
4. When the time interval between going from the past to present and then back to past to cause the gradnfather paradox tends to zero (i.e. length of the base of the triangles tend to zero), the oscillations in the timeline tends to infinity as it move to larger tau. Thus the opposite versions of histories (the "dead" and "alive" state) are only being separated by an infinitestimal amount
5. As seen by A and its hyper later copies as it look back to the past as it marches along tau, it seems what A can see in its immediate past is that everything proceed as the "alive" state with only at one instance of tau (tau=2hs in CTC scenario and tau=3hs in Primer box scenario) the history is in the "dead" state
Questions (numbered according to the observations):
1. This is weird, did I made a logical error in my deductions, or is it really what theoretically will happen given my assumptions stated above. Are discontinuities in events in time allowed?
2. This is even weird, is it really true that the ripple effect will never catch up?
3. Actually, how to interpret the physically meaning of the intersections?
4. This is pathological, how to deal with this infinite oscillating history?
5. This is also weird, did I made a mistake in my deduction?
6. Using mainstreams physics as we know it, is self consistent time travel the only solution? Is there exists any theories that can address the grandfather paradox without forbidding it to happen (other than Many Worlds Interpretaton, which some still thought it had not adequately address the paradox), or is there any concrete result that can rule out all possible types of grandfather paradoxes that can theoretically happen?
View attachment 6796
