A couple of weeks ago I was my morning train to work, tired and stressed. I didn’t want to nap on the train so I decided to close my eyes and try to focus on my breathing. It is very hard to keep random thoughts from trespassing your mind. I did ok for a bit. As I was starting to feel more rested, I recalled an image from a Nova series called Fabric of the Cosmos. The host, Brian Greene, had this great visualization of space time. He showed space time as an expanding loaf, pinched to a point at one end. The point is the Big Bang. The loaf expands forward into the future away from the Big Bang. His loaf visualizes space in two dimensions - across the width and height of the loaf, while time traverses the length.
One point of this exercise was to demonstrate that the past and future are all "real" or "there" just like all of space is real and there). This a sobering and somehow comforting idea. Moments I experienced are not gone. They’re just behind me in a 4th dimensional space time loaf.
I thought about the concept of a light cone. This is the idea that a pulse of light radiating away from you can only potentially affect things ahead of you in a region space time reachable at the speed of light. It sort of carves out a region in space and time that you can influence causally. This is hard to visualize. Imagine space and time are reduced to only height and width (2 dimensions, x and y) and now time is depth or your 3rd dimension. Now in three dimensions, the light cone points at you, and opens away from you to the future. Everything inside the cone is everything you can potentially experience, see, touch, or change. You also have a past light cone behind you which defines the region of space time in the past which could have had an affect on you now.
I thought about time travel and the grandfather paradox. The idea time travel to the past is impossible because it breaks causality. If you can return to the past, you can prevent something from happening that allowed you to get you to the past. For example, you build a time machine and go back to stop yourself from getting into the time machine. How did you get back there if you never left?
Steven Hawking illustrated this by hosting a time traveler party. He planned a date for the party in the past. Hawking sent out invitations to future time travelers (to attend the party in the past). So far there are no reports of time travelers at this party.
I realized that in Brian Green’s space time loaf a light cone might be more like a ripple in a four dimensional pond. Events in space time ripple forward as water does when a pebble is dropped. If you drop a pebble into a pond, it makes a ripple. If you drop a second pebble into a pond in the same place you make a new ripple,which never catches the first.
So what if a time traveler went back in time to Stephen Hawking's party? That event would ripple forward, affecting change ahead of it. But the leading edge of that light cone will never catch up to the ripples caused by the previous version of of the time travel party. The past is changed, but it can never interfere with the present, because the present is riding a light cone of the “original past”. There are no paradoxes, no multiple universes or “timelines” - just concentric ripples of in space time that never touch.