The Meaning of Spacetime, Relatively Speaking

June 17, 2009

Space and time are something we deal with every waking moment of the day. We need to navigate space (at least between home and office) and are subservient to time from cradle to grave. But there are inherent puzzles that stumped history’s top scientists. And, these puzzles can frustrate science fiction writers who want to find shortcuts though space and time to get from one side for the galaxy to the other within the lifetime of their characters.

Would there be space if there weren’t matter around to define a volume, like the walls of a room, or periphery of the solar system? How could we ever know that space in the universe is expanding, without galaxies flowing along with the expansion and sending us signals from the remote past? Would there be time if we never saw anything changing?

Greek philosopher Aristotle thought that Earth was at the center of the universe and therefore anchored space. In the 1600s Issac Newton equated immovable space to being a physical manifestation of God.  In the 1700s philosopher Immanuel Kant though that space and time were purely a construct of the mind.

A century ago Albert Einstein decided space and time were joined at the hip in the concept of spacetime. You can’t have space without time, or time without space. According to Einstein the universe can only be properly described in four dimensions: length width, height, and time. This is powerfully demonstrated in modern astronomy: that farther we look into space the further back it time we look (more later).

The roots of this concept go back to the puzzling but landmark Michelson-Morley experiment of 1887 which attempted to clock Earth’s motion through space by measuring the difference in the speed of a beam if light if it traveled upstream or downstream from Earth’s orbit. The result was assumed to be as predictable as comparing the speed of a bullet shot from a moving train to that of a bullet fired from a stationary position on the ground. The train-fired bullet should be the speed of the train added to the bullet’s muzzle velocity.

To everyone's amazement Newtonian physics works for bullets but not light. The beams remained a constant speed no matter what direction they were aimed relative to Earth’s motion.

This meant that the velocity of light is more than special, it is the most important quantity in all of physics. Einstein quickly grasped this and said that the only absolute value in the universe was the speed of light as seen at all times by all observers anywhere in the universe (a beautifully Copernican idea). The observed properties of light were vastly important in reshaping the mathematical models of space and time in Einstein’s theory of Special Relativity.

For the speed of light to remain fixed to all observers, fundamental values for everything else in the universe -- time, mass, dimension -- are stretchable and relative, but not absolute, Einstein said. The apparent rate of the passage of time can be throttled up or down due to the influence of gravity, or an object’s velocity across space.

For example the warping of space by a gravitational field makes time pass at a different rate. An astronaut returning from the moon comes back a billionth of a second younger than he would have been if he remained on Earth’s surface.  The GPS (global positioning system) receiver in your car would not work if the GPS satellites orbiting the globe weren’t tweaked to compensate for the relativistic effects of being embedded in Earth’s gravitational field. At the event horizon in the intense gravitational field of a black hole, time appears to come to a screeching halt. Conversely, if you were a photon of light, time would not exist. You’d circumnavigate the universe is less than the wink of an eye.

The concept of spacetime must be wrestled with in science fiction films and books. Exiting stories can be crafted around traveling backward into time or traveling faster that the speed of light. But reality is firmly anchored of Einstein’s “light cone” which gives us a reference frame for spacetime.

Light cones come in two kinds: past light cones and future light cones. Imagine a model where two funnels are glued together and their tips. We live at this intersection.  It is “the present.” Looking along one cone we look backward in time and seen ever more events, as we look deeper into space. Information from the past is dutifully delivered on our doorsteps at the speed of light. The other cone represents events yet to happen in the future.

For example, from the moment of your birth, light that you could have influenced has been expanding around the Earth.  Conversely, light that could influence you from increasing distant objects has been arriving at Earth.  This ever-growing sphere of potential causality is your light cone. If you’re 35 years old, your light cone encompasses all the stars within 35 light-years of Earth, this is the range where information about “you” can be know elsewhere in the universe, but no farther, at present.

 If you can manage to travel outside of the lines of spacetime represented by the conical surface of our model, you would be “elsewhere.”  Events would occur at velocities greater than the speed of light and hence are forbidden by Einstein. Why? The dilemma is that you could hopscotch from one event to the other in the universe and arrive at a destination before information about your departure arrives at the speed of light.

This is embodied in a cute limerick:

There once was a girl named bright

Who could travel faster than light

She started out one day in a relative way

And returned the previous night

The hypothetical tachyons, subatomic particles that would only travel faster than light, could live in the twilight zone outside of the spacetime cones. But they could never go subluminal and enter our reality by crossing the surface of the cones.

For practical reasons you can’t travel backward in time along the light cone containing information of past events. The simple paradox here is that you can’t be older than your parents.

Special Relativity allows you to travel quickly forward in time along the future light cone if you can build a spaceship that carries you within a fraction the speed of light. That’s no small engineering task.

Science fiction would be dull without inventing ways to shortcut Einstein’s spacetime architecture. But for astronomers it is sound scaffolding to build a comprehensible framework around the universe.

 

Comments

[David Parker]

Cool article!

Question...
Time travel aside, (other than that which is done by us naturally). When the speed of light is spoken of as a constant, or absolute--if light is influenced by gravity as "bending" around a gravitational field such as that of the sun--isn't it incorrect to say that it is constant in speed at all times?? If a "black hole" can keep it from escaping its gravitational "pull" doesn't this say that light can be "stopped" which is, indeed the ultimate change in speed??

I dunno, i'm just a bluecollar shop monkey!

[Pawel Strozyk]

The light still "run" as fast as possible (with full speed ;-) and as stright as possible. But the space is so bend inside black hole that those "stright" lines along wich the light travels are arcuate towards its centre.

[David Parker]

Pawel,

Are you saying that the light "orbits" the singularty, and cannot reach "escape velocity"??

Is this truely the case, or can the ENERGY not escape the center of gravity?

ANd... does light from the universe in general pour into a black hole, diverted from it's "course" as the starlight in the eclipse plates that proved Einstien's theory about gravity influencing the PATH of light thru space??

Beware... I am a high school dropout that read too many science fiction books!!

On the other hand, does light--including All of the specrum of radiation--have the same "basic" properties as matter??? (Forgive
me, but are not matter and energy hand and glove so to speak??)

[Chris Fleming]

It seems as though that is the case, but, when light enters the gravitational pull from that of a black hole, nothing can escape the horizon, not even the absolute light that had entered. But the paradox is that when the light had "entered" the horizon, escape velocity exceeding that of light, it would still be travelling at its constant or absolute speed in time, someone relative to the black hole would never see the light enter the horizon and therefore describe the light to have "stopped" but the light in the gravatational pull would go on an everlasting journey in the attemp to escape the black hole where time has relatively stopped, in the perspective of the viewer outside of the black hole, with time NEVER stopping in the perspective of the light. The question of light bring destroyed at the singularity is one that boggles the mind because lose of information would destroy the pillers of phyics, to me? I'd believe that light ever trying to escape the hands of the horizon would take an infinite amount of time to reach the singularity (infinite with all quantum physics aside, but in a sort of deterministic point of view).