What is Now?

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Shifter

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What is Now?
« on: September 01, 2020, 06:46:27 AM »
I thought this sounded cool so thought I would share

The Andromeda Paradox
https://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument

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If special relativity is true, then each observer will have their own plane of simultaneity, which contains a unique set of events that constitutes the observer's present moment. Observers moving at different relative velocities have different planes of simultaneity, and hence different sets of events that are present. Each observer considers their set of present events to be a three-dimensional universe, but even the slightest movement of the head or offset in distance between observers can cause the three-dimensional universes to have differing content. If each three-dimensional universe exists, then the existence of multiple three-dimensional universes suggests that the universe is four-dimensional. The argument is named after the discussions by Rietdijk (1966) and Putnam (1967). It is sometimes called the Rietdijk–Putnam–Penrose argument.


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Roger Penrose advanced a form of this argument that has been called the Andromeda paradox in which he points out that two people walking past each other in the street could have very different present moments. If one of the people were walking towards the Andromeda Galaxy, then events in this galaxy might be hours or even days advanced of the events on Andromeda for the person walking in the other direction. If this occurs, it would have dramatic effects on our understanding of time. Penrose highlighted the consequences by discussing a potential invasion of Earth by aliens living in the Andromeda Galaxy. As Penrose put it:

    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"?





So what is Now? What does the universe actually look like? Every observer has a different take on the universe. When we see distant galaxies we see things as they were billions of years ago. Imagine seeing the universe in its entirety, now. A snap shot of every point as it is relative to that point, right... Now!

Anyway, I enjoy mind boggling paradoxes or thoughts.
« Last Edit: September 01, 2020, 06:49:17 AM by Shifter »
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wise

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Re: What is Now?
« Reply #1 on: September 01, 2020, 07:04:10 AM »
In a way I think this debate is unreal. This is one of the things prove the absurdity of popular science.

In simpler terms, suppose a person moves at half the speed of light in his universe. At the same point with this person, another person in the opposite direction started to move at half the speed of light. The reason why we choose half the speed of light as speed is that the energy required to reach the speed of light is infinite. At least, this is the case if there is a mass.

In this case, the speed of person B relative to person A is the speed of light relatively. In other words, the energy of person B is infinite in universe A.

Well, now let's do the opposite.

There are two people on the same road. Let one of them be at one end of the road and the other at the other. Now let these people move at half the speed of light relative to the midpoint. Their speed relative to each other is relatively equal to the speed of light. So actually both cannot see each other, or they can see as light. In the universe of both of these people, the energy of the other person is also infinite.

So what happens when you collide with a mass of infinite energy? Theoretically, this could happen. I wonder if this has ever been experimented, especially in Cern.


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Re: What is Now?
« Reply #2 on: September 01, 2020, 07:22:47 AM »
An interesting example. It does raise the question of how much the concept of 'the present' means when discussing events beyond any interference.

Presumably, in the time it would take the fleet to arrive, then from the relative perspective of each person, the fleet travelled at different speeds, so you wouldn't be left in the embarrassing position of one person screaming about an alien invasion while the other has a normal day.

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JJA

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Re: What is Now?
« Reply #3 on: September 01, 2020, 10:03:48 AM »
I thought this sounded cool so thought I would share

The Andromeda Paradox
https://en.wikipedia.org/wiki/Rietdijk%E2%80%93Putnam_argument

Quote
If special relativity is true, then each observer will have their own plane of simultaneity, which contains a unique set of events that constitutes the observer's present moment. Observers moving at different relative velocities have different planes of simultaneity, and hence different sets of events that are present. Each observer considers their set of present events to be a three-dimensional universe, but even the slightest movement of the head or offset in distance between observers can cause the three-dimensional universes to have differing content. If each three-dimensional universe exists, then the existence of multiple three-dimensional universes suggests that the universe is four-dimensional. The argument is named after the discussions by Rietdijk (1966) and Putnam (1967). It is sometimes called the Rietdijk–Putnam–Penrose argument.


Quote
Roger Penrose advanced a form of this argument that has been called the Andromeda paradox in which he points out that two people walking past each other in the street could have very different present moments. If one of the people were walking towards the Andromeda Galaxy, then events in this galaxy might be hours or even days advanced of the events on Andromeda for the person walking in the other direction. If this occurs, it would have dramatic effects on our understanding of time. Penrose highlighted the consequences by discussing a potential invasion of Earth by aliens living in the Andromeda Galaxy. As Penrose put it:

    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"?





So what is Now? What does the universe actually look like? Every observer has a different take on the universe. When we see distant galaxies we see things as they were billions of years ago. Imagine seeing the universe in its entirety, now. A snap shot of every point as it is relative to that point, right... Now!

Anyway, I enjoy mind boggling paradoxes or thoughts.

Be careful not to confuse the Andromeda paradox with reality. It's a thought experiment. In reality, those two people on the street can not know what's happening in Andromeda right now. The paradox only exists because the premise of the thought experiment is they somehow "know" of events millions of light years away.

But it's certainly based on real physics. Everyone not at rest to another is in their own frame of reference, and if you start events and observers moving at high velocities relative to each other things can get very weird indeed.

Two distant observers can watch the same series of events, and disagree on what order they took place.  One observer can see A happen before B, and the other can see B happen before A. They are both right, which happened first depends on who is watching and where. So you can't ever say for sure about the order of distant events, it all depends on where you watched them happen from.  "Which happened first" is actually an invalid question, without adding "...from this reference frame."

This in fact, one reason FTL is considered impossible. Because if you could send a message FTL, then those two observers could communicate, and the one that saw B happen first could send a message to A and give them information from the future. Worse, it would allow one of those observers to travel into the past. Now you get to deal with the consequences of breaking casualty and opening up a whole can of paradoxes.

I highly recommend reading up on space-time diagrams to visualize this. Once you draw light-cones and draw it all out it starts to make a lot more sense what's going on.

Nowdays there are online tools that can help like this one: http://www.trell.org/div/minkowski.html

But start with reading up on relativity and how these diagrams work. Relativity is a seriously hard concept to internalize, but it's worth it.

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Pezevenk

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Re: What is Now?
« Reply #4 on: September 01, 2020, 12:28:48 PM »
There are 3 things that tend to really trip people up with relativity:

1) The lack of simultaneity. There is a concept of "simultaneity" in relativity but it is pretty artificial and has little to do with classical everyday notions of simultaneity. It is more helpful to just think of simultaneity as not existing. What is happening at Andromeda this instant? The correct answer is, this instant doesn't exist, there is no simultaneity. Simultaneity is mostly useful in a local context.
2) Confusing what you can see with what is happening, or the opposite. Light takes some time to reach you. People forget it and they get really confused about what is happening and what they are seeing.

Think the twin paradox. People sometimes get confused and think the moving observer will look at the observer on Earth and see them age faster. Actually as they are moving away from the Earth they will see them age slower. Then as they are moving towards the earth they will see them age much faster. Again, thinking about what age the twins are at any given time is kind of pointless since simultaneity is not a very useful concept, at least until they come back together again.

3) Relativizing acceleration inappropriately. All motion is not relative. All observers aren't equivalent. This is also true in classical mechanics. My favorite paradox in SR has to do with this, look up Bell's spaceship paradox.

There is a good book by philosopher of physics Tim Maudlin called Space and Time or something like that which explores the meaning of relativity.
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