Imaginary time

Posted Nov. 21, 2010, at 9:40 p.m.

All time exists simultaneously.
This statement, of course, appears to be absurd. As far as we can tell we live in the present, the only time that exists. To think that you might somehow still be drinking this morning’s coffee while you’re reading this article tonight, and simultaneously eating tomorrow’s supper, and tomorrow’s, and tomorrow’s, seems sort of idiotic. But according to the calculations of modern physics, all our yesterdays and tomorrows, despite our experience of now, are alive in one continuum called space-time.
How could this be.
We tend to think of time as linear, moving like an arrow in a line from the past to the future:


Yesterday                    Now                       Tomorrow

Along the line to the left are all the events, all the morning coffees, which actually happened. Along the line to the right are all the evening suppers that will happen in the future. To us, these events and moments seem like the only ones that exist.
But according to most physicists, this diagram is incomplete. All of time is not arrowing forward along a horizontal line any more than all of space is the road from Troy to Bangor. Time is a dimension, more like a block than a line. The diagram needs a vertical axis to indicate, above and below the line, time we don’t experience:



                        Yesterday                Now           Tomorrow



So we’re saying time also exists above and below the line we’re on. What time is it there?
The short answer is that no one knows. But physicists have observed behaviors of light, made mathematical calculations, and applied careful logic that indicate the time off the line does exist. And it probably includes everything that didn’t happen as well as everything that did. In other words, the whole area to the left of Now represents every morning coffee you remember having as well as every coffee you could have had but didn’t — every event and possible event that led to Now. And the whole area to the right contains everything that will or could happen.
You can draw a line from the left to represent the sequence of events that led from the moment you got out of bed to your cowlick-fuzzy walk to the kitchen and the coffee pot and everything up to Now, when you’re reading this article. The physicists call that a “world line” — the line representing a sequence of events in time. And you could continue the line on into Tomorrow to represent everything you will do leading to supper. Of course, you don’t yet know what those are. But that doesn’t stop the line from existing.
An infinite number of events could have led to Now (you might have gone to the bathroom before you went to the kitchen), and so an infinite number of lines converge from the left onto the point where you are Now, reading. After you finish reading, an infinite number of events might happen, so an infinite number of lines radiate to the right toward Tomorrow. If you were to include all those lines leading to and from Now, the diagram would look like two cones touching at the tips.
Here’s where it gets weird: Good evidence from quantum physics indicates that even though you apparently lived in just one of the possible sequences of events, where you had coffee, the others — where you went to the bathroom first or had tea instead of coffee — nonetheless happen as well. Those events are in the area above and below the time line.
Some physicists call that area “imaginary time,” which is a phrase quite titillating to your science fiction-loving mind, but it doesn’t mean what you think. Imaginary time can be calculated.
There are relatively simple formulas for computing space-time differences between two events. For example, an event happening at 1 p.m. on the Earth is about 93 million miles away from an event happening at 1:05 p.m. on the sun. Figuring the time difference of the two events is more complicated because 1 p.m. on Earth is not exactly five minutes from 1:05 p.m. on the sun. It takes light about eight minutes to get from the sun to the Earth, so the travel time changes the time relationship between the two events.
By working out a formula that includes taking the square root of a huge number related to the speed of light (186,000 miles per second), physicists can get a number that represents the space-time interval between the Earth and sun events. But if two events differ over a spatial distance that light cannot cover during the time difference (like 1 p.m. on Earth and 1:10 p.m. on the sun — more than the eight-minute light-trip between the two), then the square root has to come from a negative number — and as you might remember from algebra class, negative numbers have no square root.
The two events, though, do happen, even though their distance outstrips the ability of light to connect them in time as we experience it. To calculate that space-time interval outside our experience, the negative number’s square root is assigned what mathematicians call an “imaginary number.” That imaginary number is not on the Yesterday-Now-Tomorrow time line with real numbers. Which tells us that the two events are not connected in time as we know it. They are connected in the area above or below the time line. The math is real, and imaginary time is real.
Behaviors of light have been observed which indicate imaginary time connects and contains, not only events outstripping the light-speed distance from the sun to Earth or Jupiter, but also events that did not happen on the time line. Everything that could have happened over in the left area of the diagram, did happen, and everything that could happen over on the right, will happen. Or more accurately in block-speak: It is all happening all the time. Tomorrow and tomorrow and tomorrow all creep simultaneously, and all our yesterdays have lighted the way to untold dusty deaths and everything in between. In other words, the best scientific evidence — as infuriating as it seems to common sense — is that the whole of time and all its possibilities are one colossal Now.
This is sort of frightening in a way, because if everything happens, do I play any real role in my own life? This is a fatally important question that has to be left to philosophers. Instead, let’s ask a question scientists can reply to: If everywhen is now, why can’t we get there from here? Some physicists think it might be possible.



Read more on the nature of time:

“Time, it’s even stranger than you think”,156407

“Trapped in the fourth dimension”,156940

“Time travel: What’s holding us back?”,160722

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