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New Theories / Re: In four dimensions, must an object move at c in at least one of them?
« on: Today at 12:16:19 »
Hi.
Thanks for posting that text from Penrose, @varsigma .
I think many of us will have seen the Andromeda paradox in some form, even if we haven't read that exact text.
@Halc has already said quite a lot about it, which is perfectly good.
Of course, it's always possible to put different interpretations on SR. Usually you'll have the same final results, just different ways of interpreting it (similar to all the interpretations of Quantum Mechanics).
What is it that changes when an observer changes their own motion?
For example, an observer fires a rocket for a while and has some acceleration.
Option 1: Is it something about the observer? Something acted on them and they can know that it did because they may have an accelerometer with them. Most things in the universe were not acted on and would not have recorded anything like an acceleration. So it seems reasonable that the only thing that could have been changed is something about the observer.
Option 2: The observer wasn't changed, the rest of the universe was changed. The observer still finds that their height is 1.5 metres, their width is 0.4 metres and their wrist watch still ticks away 1 second for every "one mississippi" that they count out to themselves. All the properties and behaviours that they had before the acceleration are unchanged, it's everything else in the universe that has been changed. Distances between various things in the universe are different, some clocks tick slower or faster etc. Something acted on the observer and only on the observer but nothing about them was changed. It's been the universe around them that has had some properties and behaviours changed.
Does changing your motion change the universe OR do we assume it's only something about the observer that has changed?
That's how you ( @varsigma ) could have introduced your earlier comments. Try to hook the audience and get them to do some thinking, before you reel them in a bit.
Of course, I need to catch up a bit with what was discussed several posts ago, so I can't just end the post here. We've got to do "the reeling in" straight away.
- - - - - - - - - -
You can find ways to make either interpretation work. Option 1 is commonly taken, that's easier when you have a block universe model for 4D spacetime. When an observer changes their motion, the block universe is still the same block universe, it's just that the observer is taking a different path through it and their natural choice of time and space axis have become twisted (or rotated into each other in a complicated way). We don't change the block universe, just some properties of the observer (e.g. how they would naturally measure things and how their time and space axis are orientated).
However, option 2 is also quite interesting and can be given a suitable mathematical framework. When you change your motion, you change the universe. In the Andromeda paradox, the person walking the wrong way just had to stop, turn around and then keep accelerating away from Andromeda. If they did this, then they can live in a universe where the decision to invade will never be made. Of course people who walk the other way are in trouble, their universe is different.
This is what I think @varsigma was talking about back in reply #7:
As I mentioned earlier, Penrose is very good at discussing the Physics and the understanding or philosophy that goes with that physics. He can also provide the mathematical framework to go along with these other ways of thinking about these things. It doesn't change the overall final results but it can be of some interest that we can imagine things in diffferent ways.
You can make SR compatible with a form of presentism if you assume that changing your motion has the effect of changing the universe that you're in.
Best Wishes.
Thanks for posting that text from Penrose, @varsigma .
I think many of us will have seen the Andromeda paradox in some form, even if we haven't read that exact text.
@Halc has already said quite a lot about it, which is perfectly good.
Of course, it's always possible to put different interpretations on SR. Usually you'll have the same final results, just different ways of interpreting it (similar to all the interpretations of Quantum Mechanics).
What is it that changes when an observer changes their own motion?
For example, an observer fires a rocket for a while and has some acceleration.
Option 1: Is it something about the observer? Something acted on them and they can know that it did because they may have an accelerometer with them. Most things in the universe were not acted on and would not have recorded anything like an acceleration. So it seems reasonable that the only thing that could have been changed is something about the observer.
Option 2: The observer wasn't changed, the rest of the universe was changed. The observer still finds that their height is 1.5 metres, their width is 0.4 metres and their wrist watch still ticks away 1 second for every "one mississippi" that they count out to themselves. All the properties and behaviours that they had before the acceleration are unchanged, it's everything else in the universe that has been changed. Distances between various things in the universe are different, some clocks tick slower or faster etc. Something acted on the observer and only on the observer but nothing about them was changed. It's been the universe around them that has had some properties and behaviours changed.
Does changing your motion change the universe OR do we assume it's only something about the observer that has changed?
That's how you ( @varsigma ) could have introduced your earlier comments. Try to hook the audience and get them to do some thinking, before you reel them in a bit.
Of course, I need to catch up a bit with what was discussed several posts ago, so I can't just end the post here. We've got to do "the reeling in" straight away.
- - - - - - - - - -
You can find ways to make either interpretation work. Option 1 is commonly taken, that's easier when you have a block universe model for 4D spacetime. When an observer changes their motion, the block universe is still the same block universe, it's just that the observer is taking a different path through it and their natural choice of time and space axis have become twisted (or rotated into each other in a complicated way). We don't change the block universe, just some properties of the observer (e.g. how they would naturally measure things and how their time and space axis are orientated).
However, option 2 is also quite interesting and can be given a suitable mathematical framework. When you change your motion, you change the universe. In the Andromeda paradox, the person walking the wrong way just had to stop, turn around and then keep accelerating away from Andromeda. If they did this, then they can live in a universe where the decision to invade will never be made. Of course people who walk the other way are in trouble, their universe is different.
This is what I think @varsigma was talking about back in reply #7:
...Have you seen Penrose's description of two observers walking past each other? That this means they are literally in different 'spaces'.....
As I mentioned earlier, Penrose is very good at discussing the Physics and the understanding or philosophy that goes with that physics. He can also provide the mathematical framework to go along with these other ways of thinking about these things. It doesn't change the overall final results but it can be of some interest that we can imagine things in diffferent ways.
But Penrose assumes both a 3D spatial universe (presentism) and a 4D spacetime universe, and the paradox seems to revolve around these two incompatible models being used at the same time.Yes, it does seem that way but I think he was just leading into various different ways in which we can imagine what is happening.
You can make SR compatible with a form of presentism if you assume that changing your motion has the effect of changing the universe that you're in.
Best Wishes.