[paul cotter (OP)]

Recently "eternal student" made reference to the "Andromeda paradox". I don't get it, maybe i'm too thick or passed my sell by date! Two observers speculate on a distant(spatially+temporally) event with contradictory opinions, lets call them A and B. A could be correct with B incorrect or B could be correct with A incorrect. There will always be uncertainty about future events-what am I missing?

[Halc]

The 'paradox' is simply an extreme illustration of the relativity of simultaneity, which is fundamental to special relativity but something one might find contrary to  one's everyday life intuitions.

Two observers

Careful about this wording. Nobody is observing anything in the Andromeda scenario. It is just a reference to two different inertial frames which differ by perhaps a walking pace.

Two observers speculate on a distant(spatially+temporally) event

A pair of spatially distant events. Since one each distant event is simultaneous with the respective observer event, neither is temporally distant.

with contradictory opinions

The 'opinions' are just statements of simultaneity relative to mildly different frames, and as such are not contradictory, which is why this isn't an actual paradox.  The scenario does not involve empirical measurements of any kind.

A could be correct with B incorrect or B could be correct with A incorrect.

They're both correct. Neither says anything that contradicts the other.

There will always be uncertainty about future events-what am I missing?

There is no mention of a future event here. Both A&B are making statements about a current event, something that cannot be measured since one can only measure something in the past if it has any spatial separation from you.

So relative to frame A, the Andromedons have not yet decided to make this attack, and relative to frame B, the Andromedons are currently in flight with their battle fleet. Neither statement contradicts the other.

This only seems paradoxical since one's intuitions tend to assume absolute simultaneity where simultaneity is not frame dependent, and thus the above statement reduces to: The Andromedons  have not yet decided to make this attack and the Andromedons are currently in flight with their battle fleet. That statement is contradictory, but under SR, it is not even wrong since it lacks frame references.

[Eternal Student]

Hi.

    Hope you are well.   This is is obviously one of the most interesting posts available today.  I have a strong suspicion that @Halc is about to write a post since the forum is reporting him as viewing this post at the moment.    He obviously has a head start over me, so I'm just going to wait and see what gets done.
      For the short term, I'm just going to glance through some YT videos that might exist and see if I can recommend one.

Best Wishes.

[Eternal Student]

Hi again.

   Well done @Halc .   I also can't find a good YT video for the Andromeda Paradox.   There are videos but none of them great.   If anyone else knows of a good YT video that would be of interest to me (even if no one else).

    This might be something we explain from first principles.

Best Wishes.
     

[paul cotter (OP)]

Eternal student, I hope you are well, you did mention the dreaded covid. Halc, I would argue that the two participants have contradictory positions: one says the decision has not been made yet and the other says the fleet is in transit already. I must admit to not having read the wiki explanation very thoroughly and I missed the point where the travel of the fleet is a foregone conclusion. I still don't see anything of value in this.

[Eternal Student]

Hi again.

    Well look, here's the thing from first principles...

    Start with a person called Paul on planet earth.   For ease of notation and calculation we will set up an inertial reference frame S  with co-ordinates (space, time) = (x,t) .  We'll only need one spatial dimension (just choose a Cartesian frame so that planet earth and the Andromeda galaxy lie along the x-axis).  We'll have Paul stationary in the frame S and, as usual, we'll put him at the origin.
    To keep it all simple, we'll have the Andromeda galaxy at a distance of  3 million light years from earth and we'll have it remain stationary in the frame S.     (In reality it's about 2.5 million light years away and you probably know it's on a collision course - none of that's necessary for the Andromeda Paradox, we just need it at a large distance).

    Let's draw a spacetime diagram now and put some important worldlines on it.


Andromeda1.png (12.8 kB . 1304x767 - viewed 1335 times)

   Since Paul and the Andromeda Galaxy are stationary in this frame, their worldlines run parallel to the t axis.   Paul's is precisely along the t-axis.

    Now the general idea is that there are some Aliens living in the Andromeda galaxy and they will decide to invade earth.    Let's mark some important events on the spacetime diagram.     Event (x_A, t_m )   =   where and when the Andromedans have a meeting to consider invading Earth.       Event  (x_A , t_L ) =  where and when the Andromedans launch the invasion fleet.
   Paul considers events lying along the x-axis to be events occurring at time t = 0,  or  "right now".   So, for Paul,  the Andromedans are having a meeting to decide if they will invade.


Andromeda2.png (12.89 kB . 1304x767 - viewed 1335 times)

   Now Paul has a friend,  let's call them Bicycle Brenda,  who is riding a bicycle past Paul at a low speed and just happens to be travelling toward the Andromeda Galaxy.   So Let's consider how Brenda sees the universe next...
   This is just standard stuff in Special Relativity,  Brenda sees Paul looking slightly thinner than if he was at rest,  this is length contraction  etc.   However, since the speed of Brenda relative to Paul is so small, it's not like this really matters or is significant.   Anyway, the easiest way to determine how Brenda sees the world is to construct another inertial frame around Brenda where she is the one at rest at the origin.   We'll set up a second frame S'  in which Brenda is at rest and at the origin.   We'll synchronise the times t and t' = 0 when Paul and Brenda are precisely at the same place (I'll say just passing each other but for the Mathematics it will fine if Brenda has ridden right through Paul at the event t=t'=0 and x=x'=0).   Anyway,  the frames   S with co-ordinates (x,t)   and    S'  with co-ordinates (x',t') are just Lorentz boosts of each other as usual,   with a tiny off-set velocity v = bicycle speed = 2 mph.

    We need the Lorentz transformations to see how the events in S are mapped to events in S',  we'll just focus on the time coordinate t'

t'  =   
   You can check this equation yourself, see https://en.wikipedia.org/wiki/Lorentz_transformation , for example.  Spend a moment and remind yourself how this equation can be used.    Given an event with values (x,t) specified in the frame S,   this equation determines the t' value that would be assigned to the corresponding event in frame S'.    We could determine the corresponding x' value with another equation - but we won't need that for this example. 

    Brenda considers all events in the universe to be happening "right now"       if and only     they have t' coordinate = 0 in the frame S'.    They can have any  x' co-ordinate (that just tells her how far away the events are in space),  just so long as  t' =0  (that means they are happening at t'=0 or right now, where "now" means when Brenda passed Paul and said "Hi!"  or  "Sorry I just ran you over" etc).
    We want to mark all the events on our spacetime diagram that are happening right now for Brenda.  However, our spacetime diagram only has an axis marked up for the frame S.
    Set t'=0  in the above Lorentz transformation equation and determine the set of all events (described with co-ordinates  x,t in S) that are happening "right now" for Brenda,  that's what we will mark on our diagram.

   From the Lorentz transformation equation we obtain:
0 =  t'   =      
   ≠ 0    ,  so divide ,   re-arrange and obtain 

  t' = 0        <=>        t = 

On the R.H.S.   we have the relationship  between  t and x  (the co-ordinates in S  that describe events happening now throughout the universe for Brenda.
    v =  small positive value =  bicycle speed in S and it's in the +ve x direction.
    c²  =  a massive number.

v/c²   is therefore a tiny positive number.      t =    (v/c²) . x   describes a straight line on the diagram that is almost parallel to the x-axis.   However the key is that it is NOT quite parallel to the x-axis, it is angled upward a tiny bit.   Moreover the Andromeda galaxy is a long way along the x-axis, so let's  put this line of constant  t'  on our spacetime diagram and see what happens.....


Andromeda3.png (16.34 kB . 1304x767 - viewed 1337 times)

   The Green line shows all the events throughout the universe that are happening now (t'=0) for Brenda.
Hopefully you can see that, as far as Brenda is concerned, when she passed Paul and said "Hi!"  the invasion from Andromeda has been launched.   Meanwhile, for Paul the meeting to decide whether to invade Earth or not hasn't finished yet.

Anyway, I hope that will help to see the gist of the argument for the Andromeda paradox.
As @Halc mentioned earlier,   you need to be carefull not to say,  Brenda "sees" the invasion has been launched.    There's no way light has reached Brenda's eyes yet, she isn't going to "see" the ships coming.   It's only that the launch is actually happening now for Brenda even though there is no practical way she could know.  So, for example, she couldn't tell Paul that it was coming.... unless she has some  extra-sensory perception and says "you know, it's funny but every time I ride my bike in that direction I just feel like some invasion has been launched".  In which case Paul would reply, "have you tried changing to a lower gear?  You might be getting yourself a little out of breath and dizzy".

Best Wishes.

[Eternal Student]

Hi again.

Eternal student, I hope you are well, you did mention the dreaded covid.

   Yes, I'm much better today, thanks.  Nearly running at normal temperature - if my earlier posts were still a bit weird then that will be why.    I'll still be stuck at home for a while since I'm now caring for family members who are a few days behind me in the progression of the disease.   We're all vaccinated and not especially vulnerable to respiratory problems, so it should all be OK.

Best Wishes.

[Halc]

Halc, I would argue that the two participants have contradictory positions: one says the decision has not been made yet and the other says the fleet is in transit already.

Yes,l those statements are contradictory, but neither of them says those things. Both statements presume absolute simultaneity by their omission of frame references, and it can easily be shown that neither postulate of special relativity can be true if the premise of absolute simultaneity (an intuitive assumption) is taken.

Part of the confusion is the statement of something not measured: 'The Andromedons are considering whether to attack' for instance is not something that anybody has measured. It is simply an abstract statement, a description of the scenario in question by the narrator so to speak. No observer can measure this, certainly not A and B. Likewise, if Andromedons are somehow considering an attack on Earth, it isn't against humans since there's no way they could have yet measured a species yet to have evolved. We are no more fact to an Andromedon obesrver than they are fact to us.

[paul cotter (OP)]

Thank you, eternal student, for your detailed reply. I can follow your reasoning explicitly, however I can't grasp the concept, if that makes any sense. Bottom line: I think I have covid too. I had sudden onset low back pain and brain is not in gear and i'm making mistakes in everything I do. I will return in a few days(hopefully).ps i'm fully "vaxxed" as the conspiracy theorists would call it.

[paul cotter (OP)]

Halc, as explained to eternal student, i'm temporarily dropping out of this discussion.

[Eternal Student]

Hi.
    No worries @paul cotter ,  rest up and get well soon.
Best Wishes.

[Halc]

I think I have covid too. I had sudden onset low back pain and brain is not in gear and i'm making mistakes in everything I do

I second ES's wishes. Take time off and get your ducks back in a row.
Take care, Halc

[alancalverd]

 

as far as Brenda is concerned, when she passed Paul and said "Hi!"  the invasion from Andromeda has been launched.   Meanwhile, for Paul the meeting to decide whether to invade Earth or not hasn't finished yet.

When did you become a Downing Street spokesman? 

[Colin2B]

I can follow your reasoning explicitly, however I can't grasp the concept, if that makes any sense. Bottom line: I think I have covid too.

Yes, I can see you are thinking how can you answer the little voice in the back seat saying “are we there yet?”

Get well soon and I’m sure the brain fog will clear, but we might need to take a step back and examine how you first came to terms with the fact that there is no absolute spatial reference.

[Eternal Student]

Hi.

   I've still been looking for a good YT video.   I can't find one but this one seems close enough and reliable.
It's an extract from    "The Fabric of the Cosmos The Illusion of Time",  featuring Brian Greene.   That seems to be a paid-for documentary but there's a 9-minute section of it on You Tube for free.   (I don't know if it should be there, someone else put it there and I'm going to guess Google would have removed it if they should have done).

    The section between 3:54 and the end (approx. 9:40)  presents the ideas (without any mathematics) that suggest a block universe.

   That's something you could watch and not need to worry about or concentrate on too much.

Best Wishes.
   

[Dimensional]

I am totally confused too.  Here is the original quote from Penrose (taken from Wikipedia),

Two people pass each other on the street; and according to one of the two people, an Andromedean space fleet has already set off on its journey, while to the other, the decision as to whether or not the journey will actually take place has not yet been made. How can there still be some uncertainty as to the outcome of that decision? If to either person the decision has already been made, then surely there cannot be any uncertainty. The launching of the space fleet is an inevitability. In fact neither of the people can yet know of the launching of the space fleet. They can know only later, when telescopic observations from Earth reveal that the fleet is indeed on its way. Then they can hark back to that chance encounter, and come to the conclusion that at that time, according to one of them, the decision lay in the uncertain future, while to the other, it lay in the certain past. Was there then any uncertainty about that future? Or was the future of both people already "fixed"?

— Roger Penrose, The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics

I understand that this says nothing about this being a physical paradox especially when considering a block universe.  But it is Penrose saying this, so I am trying to understand what he thinks is paradoxical.

Does anyone understand what he might be getting at?   

[Eternal Student]

Hi.

    There's nothing literally "paradoxical",  it's just meant to make you think about or re-consider a few things:   How you imagine time; how uncertain the future might be and if events do disappear or cease to exist once they are in the past;  and similarly if events in the future don't exist yet.

      It might help if you consider the situation from Andromeda.   Instead of you and your friend being on Earth and walking past each other, consider an Andromedon called Andrea and her friend, Billy-Andrew, walking past her on the streets of a planet in the Andromedon galaxy.   
    Now you are still you on planet Earth.  As a sensible human being you would assume that you have a freedom of choice about whether to invade Andromeda.  According to Andrea, you are currently making a decision about whether you should go to war against the Andromedons.   According to Billy-Andrew, the decision has already been made and the Earth fleets are on their way. 
     Now, just consider yourself on planet Earth, at the moment when you are deciding whether or not to go to war.  Is it possible that you can decide not to go to war against the Andromedons?   As an ordinary human being you would imagine this is still undecided,  the future invasion is not determined,  that future does not exist yet.    However, for Billy-Andrew your decision has already been made and the invasion has been launched.    If you can and do decide not to go to war, then that should be the events of the present for Billy-Andrew.

     There are two, slightly separate issues, that might raise concern for us (human beings):

1.    That events which are in our future actually exist in the present for at least one of the aliens.
2.    That we (human beings) didn't actually seem to have any freedom of choice -  the results of our decisions are in the aliens present (provided we select an alien far enough away and moving the right way).   Indeed it was not possible for you to have reached any other decision.

    The Free Will concerns are, naturally, of considerable interest in Philosophy but not directly relevant to the notion of a Block Universe.
    The idea marked 1. - that events in your future actually exist as events in the present for an alien is all we need to start supporting the notion of a block universe.   We can show (just by having the alien move in the other direction), that events in your past are also equally real and exist.  They are happening right now, in the present, for that alien.   

    There's no especially good reason to decide that an event "existing" must or should be demonstrably shown to be an event that is happening now or "in the present" for someone.   However, that is one reasonable way to show that an event "exists".    For example, someone can argue that all you know is that there are some events happening around you now, that's all you can be certain exists.

Best Wishes.

[Halc]

I am totally confused too.  Here is the original quote from Penrose (taken from Wikipedia),

Two people pass each other on the street; and according to one of the two people

This wording "according to one [person]" means, 'relative to the inertial frame in which this one person is stationary'.  In this sense, the two statement are entirely non-contradictory and there is no paradox. Each person realizes that the current Andromeda event relative to the frame of the other person is a different event than the current Andromeda event relative to himself.

... the decision as to whether or not the journey will actually take place has not yet been made. How can there still be some uncertainty as to the outcome of that decision?

Penrose is apparently a presentist. One cannot use tensed language like this when describing a model where there is no ontological separation of events into past, present, and future. So Penrose finds the paradox not between the two view of the different observers, but between special relativity theory and his presentism. Yes, these two premises do indeed contradict each other.

If to either person the decision has already been made, then surely there cannot be any uncertainty.

Under a block view, there is a certain kind of determinism, and thus no concept of the sort of uncertainty that Penrose is referencing here. That uncertainty is only something that comes from a presentist premise.

I understand that this says nothing about this being a physical paradox especially when considering a block universe.  But it is Penrose saying this, so I am trying to understand what he thinks is paradoxical.

Correct. Special relativity premises imply a block view of the universe (no ontological difference between events), so he's finding this difficult (impossible) to meld with his alternate interpretation of time.  Under presentism, neither premise of special relativity can be true.  Physics is different from one frame to the next, violating the first premise. And speed of light is frame dependent, and is c only in one frame.

Nobody has ever generalized a theory based on the alternate (preferred frame, or absolute physics) premise. That does not itself mean that presentism is wrong, only that nobody has done the work starting from that alternate set of assumptions. Neo-Lorentz-aether theory attempts it, but they've not done the work. All they say is to use Einstein's equations for all predictions, and also, those equations are based on false premises and are thus wrong.  LOL.

[paul cotter (OP)]

Eternal student, all is clear this morning though I don't feel 100% yet. It's simply two participants(halc won't allow observers-he's correct) in different frames disagreeing on the timing of an event. My malfunctioning engineering brain viewed the two frames as being sufficiently similar as to consider them equivalent. A higher speed of one participant would give a greater slope to your green line. The wording in the wiki article(penrose's version) still 'hurts' my brain. Many thanks again.

[Eternal Student]

Hi.

I'm glad you're getting better @paul cotter .

A higher speed of one participant would give a greater slope to your green line.

   Yes, that's absolutely correct.   However, that's not where the emphasis is usually placed.
The emphasis is usually put on the massive distance between Earth and the Andromeda galaxy.   As such even a tiny slope on the green line results in a huge difference in deciding which event is happening now in Andromeda.
 
  So, the common development of the Andromeda paradox is that even if you did something like just turn or shake your head in different directions,  that slow movement is important when magnified over huge distances.   It's an effect of special relativity that doesn't require space rockets and travel at speeds close to that of light etc.

Best Wishes.