It's a New Year! — Ready for a blog posting about time?
I’ve been seeing numerous questions online that involve coming to grips with the “look-back time” of many of the deep space objects we image with our smart scopes. Anytime light is involved time and events becomes relative. Unfortunately, we can’t time travel in one of H. G. Well’s imaginary machines just yet, but with telescopes we are always receiving information from the past and are therefore, in perception at least, time traveling.
Of course even when we see light from across the room we’re looking at light that is ten nanoseconds old. And with Solar System objects we’re only dealing with delays of seconds to an hour or so. For the simpler telescopes of my past, this was not an issue. But now with my smart telescopes, I can routinely perceive objects millions to even a couple billion light years away. This is truly deep time.
This blog entry is to bring you up to speed with one way I’ve found useful to conceptualize this deep time connection — at least for distances up to about a 200 million light years. That’s when the Jurassic Period began here on Earth.
Why 200 million? That way I don't have to take into account the expansion of the universe in this entry. The reason is that the universe only expanded about 1.4 % since that time period, so any cosmological effects we might run into see will be slight. I think it’s therefore best to start with static time frames that don’t go back much further than the creatures we would have seen in our real “Jurassic Park.” (Sometime maybe I’ll write a posting about how to think of this with the expanding universe for objects billions of light years away.)
We’re therefore going to deal here with what’s called “flat” spacetime that is static. We will need to understand five concepts: 1. spacetime diagrams, 2. light cones, 3. cosmic pictures, 4. cosmic maps and, finally, 5. world lines. I’d normally call 3. & 4. world pictures or world maps, but I think cosmic works better and is more fun. The basic idea behind the pictures/maps distinction was made by the English astronomer E. A. Milne back in the 1930s.
SPACETIME DIAGRAMS
The most useful concept to help us think about our observing is to understand spacetime diagrams. When Albert Einstein knitted occurrences at specific locations and times (AKA, events) together with the speed of light, physicists haven’t been able to really untangle the four dimensions we live in: 3 of space and 1 of time. The first spacetime diagrams were developed by Hermann Minkowski in the early 20th Century shortly after Einstein wrote his papers on Special Relativity.
The above spacetime diagram places the observer at the origin. The vertical time axis goes forward in time (upward) or backward in time (downward). This diagram can only handle two dimensions of space. We could think of them as x and y or a plane slicing out into the sky. To show the third spatial dimension, z, we’d have to look at it from a fourth dimensional perspective. So far, we’re not able to do that in pictures. With math it’s quite easy, however, though we won’t go there right now.
Technically, the present time in this two dimensional world is represented by what’s called the hypersurface of the present. I’m not too keen on the hypersurface language and would prefer to think of this surface as our present “cosmic map.”
A key feature of a Minkowski diagram is that we only detect events from great distances that are on our “past light cone.” That’s the route of light from very far away. But you’ll also notice that the farther out light travels starts on the cone, that farther back in time it is. This cone is our connection to the universe through light. The past light cone represents our “cosmic picture.” But let me try to illustrate what’s going on by explaining these concepts further.
Though H.G. Wells invented other future species, like the Morlock, in his famous novella “The Time Machine,” we can only relate to the past with our telescopic time travel. So, when the galaxy M51 emits light that travels to our telescope that happened at a specific location in space, but also at a time 23 million years ago. We do not see what M51 looks like today — January, 2024. Back when the light you image tonight was emitted our closest primate ancestors were a species similar to Victoriapithecus, that weighed about as much as your smart telescope. (N.B.: At the end of this blog entry I have a handy table of some of the Earth fauna that were running around when the light from different objects was emitted.)
So, the first principle of space time thinking is, what you see is not what you get if you were at the object right now. What you see is what has arrived in your telescope the night you are observing. Astronomers, if they had existed, 50 million years ago would have seen see something a good bit different. They would have seen M51 as it was 73 (=50+23) million years ago.
COSMIC PICTURES & COSMIC MAPS
I find it useful to think of a simpler analogy for what we actually experience — cosmic picture — and what our brains would like to think we see: the cosmic map. To help visualize this analogy, we will do a thought experiment on more familiar territory – the USA.
A current road map of the United States is one that contains cities, roads and other features, all of which are contemporaneous — sort of like a hypersurface of the present. The time would be the present publication date of the map.
Practically speaking one wants to have the most up-to-date road map. If one tried to drive across the country visiting cities along the way, a map from 1926 would be of little use. It is natural to think of our spatial world being analogous to a road map. With astronomy, however, it is as if we have a stack of maps to deal with. With farther objects it is as if we are confined to older and older maps.
And, matters can become even worse. We only see a portion of the distant maps corresponding to the exact time delay for that distance. Furthermore, different people in different locations see different situations. Welcome to relativity! Again, this is the basis of the concept of a cosmic picture. Our thought experiment cosmic picture of the United States might help to make this point clear.
To understand this illustration, we will start our thought experiment atop Mt. Palomar Observatory in Southern California. The time is the recent present, say 2006. Furthermore, assume that we could use the observatory’s Hale five-meter telescope to see locations in the continental US. (The atmosphere and the curvature of the earth are the least of our problems in this thought experiment!) To make this analogy strictly parallel to the cosmology, now consider what it would be like if the speed of light was only 20 km/year! That’s very slow, but not unimaginable. This image then outlines schematically what we would see.
The three black circles correspond to distances from Mt. Palomar of simultaneous past events. The first circle is the ring from which events from 1945 are just beginning to reach the observatory. On this ring the first atomic bomb test would be occurring in New Mexico. Ring two, three times farther away, corresponds to a date around the time of the American Civil War, 1861. At this distance, the telescope would be seeing, for example, the battle of Wilson’s Creek in Missouri. The Confederates won that first battle west of the Mississippi river. Way out at the eastern edge of the continent, the telescope is just getting information of events in Massachusetts, in particular the midnight ride of Paul Revere on April 18, 1775. This cosmic picture is due to this slow speed of light we have imagined. From the west coast this speed would show selected events from the entire history of the United States!
A way to see how this cosmic picture is constructed is to imagine a series of cosmic maps including events for every year of the United States as shown below. If the maps were stacked, then what is actually seen in the picture could be determined by slicing a cone back through the stack of maps. The light cone, then would grow in radius by 20 km every year until it reached all the way to the East Coast. Where this cone sliced the different maps would determine what the telescope saw for that particular map epoch. The events that make up the world picture fix times with locations. So, the picture would be entirely different if one were to put the Hale telescope in Chicago.
Of course the previous example is only a thought experiment. But it illustrates what we are dealing with in astronomy. We will now describe the concept of cosmic map and cosmic picture with diagrams of the wider universe. Again, we will only deals a static universe, like our US map here. That’s okay because we’re not seeing super far, like the JWST sees.
SIMPLIFIED SMART SCOPE SPACETIME & OUR WORLD LINES
Next, here's the type of diagram that I find most useful to think about in practice. It has just one distance along the bottom. It’s actually the radial distance from our scope out to any specific object. In this image although I haven’t shown numbers, it spans 200 million light years.
Then for the vertical axis I’m using millions of years. It goes back 200 million years too. Thus, the relevant part of our past light cone, has a slope of minus 1. I’ve shown the arrows on the cone to describe how the light from these distances is traveling towards us all the time.
We’re at the upper left corner. That’s our present point in time and space for our observing. The vertical line we’re on is also called a world line, because that’s were we’re going even if we’re not moving in space. We’re always traveling forward in time even if we’re too tired to get out of our easy chair.
Each of the three galaxies I’ve drawn on the diagram are at a different distance in space, but they too are traveling through time and have their own world lines. Where their world lines intersect our past light cone is the point in time when the light we see in our scopes left. You could thus read those times off the left hand vertical axis if I had written in the numbers.
An important thing to realize is that the current (one dimensional) world map of this diagram is just the horizontal line at the top. This is the present state of these objects if we could see them at this instant as if we had a super-luminal telescope. No doubt they would all look somewhat different.
But alas we can’t jump through hyperspace the way science fiction can. I console myself by trying to image what life was like back here on earth when the light from these galaxies was emitted. Below is a handy table.
CONCLUSION: TIME TRAVEL, BUT ONLY FORWARD INTO THE PAST
Speaking of the past, way back in 1989 or so, when I would commute to Chicago’s Adler Planetarium on the CTA, I used to see people reading Stephen Hawking’s book, “A Brief History of Time.” (Chicago is a very physics conscious city.) At the time I was ultimately responsible for the Adler's adult evening course program so I thought, “Why not teach a course on Hawking’s book?” At first my planetarium colleagues were a bit skeptical. But, the class filled with well over 100 attendees the first time it was offered. It was inspiring to teach and challenging at some points, but the audience and I had great fun learning about spacetime and cosmology.
Attending the first course offering was a tall, older man who always dressed in a long coat. Near the end of the term he said he wanted to talk with me privately after the last session was dismissed. I said yes. When the room that final night was cleared he slowly opened his trench coat slightly to show me a small circuit board filled with resistors, capacitors and other electronic components. He then said sotto voce, “This is my time machine” and quickly closed his coat before I could get a good look at it. Ever polite as I usually am, I replied, “That’s very exciting. So, where in time have you been?” He huffed, “It’s not finished yet!” Then added I was not to tell anyone, turned, and scooted off for the lecture hall's exit.
I said, “Okay" as he drifted from sight. I have kept his secret until now since I’m sure he’s long gone one way or the other. I sometimes imagine he succeeded escaping our present hypersurface and is now living in some far distant time. You might think I'm kidding, but in my memory he looked a bit like Christopher Lloyd from the film Back to the Future.
Even though my time traveling student wouldn’t share his tech, I now tell myself that telescopes are like time machines. With my smart scopes I finally have some so I can at least continue going Forward into the Past!
Here's wishing you all clear skies and ample battery power in the New Year.
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