The Flow of Time
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December 25th : The Flow of Time
Quote of the Day
"... one second per second is one second divided by one second, and one second divided by one second is the number one. But the number one is not a rate, so it is certainly not the rate at which anything (the flow of time included) happens."
-Bradford Skow, “One Second Per Second” Philosophy and Phenomenological Research (2012).
Thoughts for the Day
For the last two days, we have contemplated the unintuitive geometries of direction on a sphere and four dimensions. We have explored how these might apply to the 'beginning' of our universe and to time. We pretended to move back and forth around the place where the direction, past, ends. We used this thought-experiment to think about how time started, one of the Big Questions of metaphysics. Today we will consider another such Big Question. 'What is time and what makes it flow?' Let us begin by thinking about how we could actually achieve the movements, in reality, that we pretended yesterday. If we could move in such a fashion, back and forth through time, how would we measure the rate of our movement? As Bradford Skow points out in the quote of the day, one second per second is not a rate.
Of course, relativity talks a great deal about time dilation. In relativity an event is a 'place' in space-time so you might say that "yesterday noon local time at Cape Canaveral" was Event A or "tomorrow 9AM local time in Death Valley California" is Event B. A path through space-time is defined both by the places it visits along the way and the times it gets to each place. In time dilation, two alternate paths can lead from Event A to Event B and yet take different amounts of time to get there. We would say that the time between Events A and B is 48 hours but that is only because we spend a great deal of time traveling through very flat space-time. If we went by more adventurous paths the time between those two events might be 4 hours or 800 hours or any other amount of time. This means that, in relativity, one might say that along one path time passes at 2 seconds per second of time that passes on another path.
In order for us to actually travel back and forth around the beginning of the universe, we would need to use some very adventurous paths indeed, something akin to worm holes in space-time or warp drives would be needed. But what about the normal 'traveling' through time that we do every day. We start our day in the morning and by evening its ... well its evening. We seem to flow through time from morning to evening every day and then from evening to morning every night. What is powering this flow? Does everything in the universe have some kind of temporal inertia that keeps it gliding evenly forward through time at one second per second?
Bradford Skow's answer is that the flow of time is an illusion. In fact, many physicists believe that objects do not flow through time but are present at all times between their creation and their destruction and that they form a kind of 4 dimensional worm that stretches from their creation event to their destruction event. This agrees with all our imaginings of time travel. If all objects were gliding forward through time at a constant rate, and if you managed to send a DeLorean back in time from 1985 to 1955 then you would find an empty universe. Everything would have already moved through 1955 and on past 1985. You would find an inky black cold universe. If it is possible to go back in time and find Doc Brown recovering from a fall in his bathroom, then Doc Brown, his bathroom and the Earth all must still be in that event in space-time 'when' another 'temporal part' of Doc Brown is oiling his new DeLorean at an event in space-time we would call 30 years later.
Relativity does predict that time-travel is theoretically possible. All you have to do is warp space-time is some very exotic ways in order to form a worm hole through to another part of space-time that is in your past. Warping space-time is easy enough; every mass warps space-time; you warp space-time every time you walk over to the fridge to get a glass of milk. But warping it in the exotic ways necessary to create a worm hole is beyond us. It's not just that we don't have powerful enough machines to do it; we don't even know what a machine capable of doing it would look like. Still every prediction that relativity has made that we have been able to test has been right to many decimal places, so we might assume that it's predictions about time travel are also correct. Relativity also predicts that the objects that were there at any time in the past (even 1955) would still be there if you travelled through a worm hole to the past so the objects must actually be present at all times between their creation and their destruction just like the 4 dimensional worm image we discussed in the previous paragraph.
Contemplation for the Day
If you can, perform this contemplation in a corridor where you can stand and walk several paces in a straight line. You can also do this outdoors, if you have no place indoors that you can do it.
Our minds are poor when it comes to imagining 4 dimensional objects. The best we can usually do is to ignore one dimension and picture the 'extra' dimension as the one we are ignoring, a sort of mental dimensional swap. So let's imagine for a moment that up is the future and down is the past.
Start in the corner of your room facing the middle or at one end of your corridor facing the other and take a single slow smooth step forward. Now look behind you. You don't see yourself! But if the 4 dimensional worm theory of objects in time is true then another temporal part of yourself is still there but a second or so in the past. If we are performing our mental dimensional swap such that down is the past then that other temporal part of yourself is under the floor somewhere.
But your step forward was not a matter of you disappearing from one place and appearing at another place a few seconds later. You moved forward smoothly occupying all the places between your starting point and where you are standing now as the second passed. So all the 'places' in space time between the temporal part of you now who is looking back and the temporal part of you who began to step forward would also be occupied by temporal parts of yourself. It was a smooth movement so, at least at the macroscopic scale, all these parts would be connected together in a diagonal that emerges from the 'floor' and smoothly rises up to connect to the temporal part of you who is looking backward. Of course all the spatial parts of the floor would also have temporal parts sloping downward behind you but, in the hope of being gentle on our minds, which have enough trouble with 3 dimensions, let's not try to imagine that.
All these temporal parts of yourself each have all of your physical parts; your arms and legs, brain and heart, eyes and ears. Each physical part flows smoothly through all of your temporal parts. Your right eye in one temporal part is always connected to your right eye in the next temporal part. Your right eye never suddenly becomes your left kidney. Your heart in one temporal part of you connects directly to your heart in the next temporal part of you despite the fact that both temporal parts of your heart are completely surrounded by different temporal parts of your torso. These two hearts are connected without having to exit your chest at any 'time in-between'. This is hard to picture because it happens in four dimensions and we are only good at picturing 3 dimensions. The best you can do is to kind of blur your image of yourself so that you become a kind of ghostly cloud of a person stretched forward and diagonally upward. What we are doing now is actually transposing two dimensions on top of each other; your head is physically above your feet and your future self is above your past self. By transposing the two dimensions so that we can see both your head and your feet and future and your past, we also create the ghostly blurring of yourself. The alternative would be to picture a thin slice of yourself, perhaps a thin horizontal slice of your belly moving through time but that wouldn't be very pleasant.
Now look forward again. Imagine that in the near future you will be continuing your journey across the room or along the corridor. The temporal parts of yourself who will be making that journey will be 'already' there but climbing into the ceiling of the future forming a diagonal that stretches perhaps several stories upward into the future before you reach the far end of the corridor or side of the room. All these temporal parts of you are connected together into a single stretched out segment of 4 dimensional human-worm.
It isn't too taxing to imagine this short section of your life as a sloping stretched out human being. But how can you imagine your whole life, as you wander around the world back and forth to work and on trips to visit your relatives, as you eat food and breath out carbon dioxide and as atoms join your body and leave it, as you have children and their bodies leave yours and start their own journeys and as you emerge from your parents and they from your grandparents.
It all gets messy and complicated. Simplify the picture so that your mind can hold it. Focus on your own body shrinking as you mentally 'follow' it back through time into your childhood. Picture your body as the blurred together chain of temporal parts tapering as you go back through your childhood to your infancy. Forget about the crazy twists and turns that your body makes as each day you go back and forth to school or daycare. Simplify and focus on the change in your bodies size tapering down from many feet tall to perhaps just a single foot, still human shaped but narrower than the temporal section of you that we call your adulthood. As we move back through the moment of your birth, you reach the narrow section of you where you were called a fetus. Now akin to how we described your heart, each temporal part of you is directly connected to the next while at the same time entirely surrounded by separate temporal parts of your mother's womb. There is no separation between you the infant and you the fetus. You are a single connected 4 dimentional worm.
Follow the four dimensional blur of the temporal part of yourself that is you as a fetus backward in time as it tapers down to a single cell and merges with your mothers ovary. You are still there, a single cell line within your mother's four-dimensional space-time body but blurred beyond recognition. Again there is no separation between you the zygote and you the cell in your mother's ovary. From your adult self all the way back to that cell is a single four-dimensional object. You are literally a branch of your mother; the same object as your mother in four dimensions. You seem like two objects now because you only see the temporal parts of your mother and you that intersect with the time we call now. But if you both stretch back through time as four dimensional worms to the point where you were part of her body then you are just connected parts of the same object in space-time.
Follow your mother back as she shrinks down into infancy and becomes a single cell line in your grandmother. That cell line isn't just your mother. It is also you. If you have siblings it is also them. That cell doesn't somehow become all these separate people. It is them. They are all a single connected four-dimensional object that stretches through space-time. Each child emerges from its parent like a branch emerging from a trunk. Somewhere back in each child's past, it is still connected to the four dimensional blur that is its parent.
Now imagine this line stretching back through a dozens of ancestors several millenia. Hundreds of branches come off this temporal worm and most of those branches themselves becoming more and more worms until they account at the present day 'end' for our whole human population. This isn't a family tree. It is a single four dimensional object. Humanity is not just a group of related people. It is a single four dimensional object. We are not just all brothers and sisters and cousins as we are taught by geneticists. We are all one object when viewed through the eyes of a temporal physicist.
Now imagine the stretching of this branching line further into the past to the common ancestor with all the other mammals. We are not just related to the other mammals. Mammalia is a single four dimensional object. And on further into the past to the common ancestor with all other animals. We are not just related to all other animals. Animalia is a single four-dimensional object. And on further into the past to the common ancestor with bacteria. All life is not just related. All life on Earth is a single four dimensional object of which we are each but a segment or branch.
Quietly contemplate this idea for a while. Open your mind to being one object with the body of all life.