Relativity and Quantum Mechanics

The general theory of relativity and quantum mechanics are the two most fundamental theories of physics, and the Big Bang theory is the leading theory of cosmology.

According to relativity and quantum mechanics, spacetime is, loosely speaking, a collection of points called "spacetime locations" where the universe's physical events occur.

Spacetime is four-dimensional and a continuum, and time is a distinguished, one-dimensional sub-space of this continuum.

Any interval of time--any duration--must be a linear continuum of instants in which one event follows another from past to present to future.

So, a duration has a point-like structure similar to the structure of an interval of real numbers; between any two instants there is another instant, and there are no gaps in the sequence of instants.

This first response to the question "What does science require of time?" is too simple. There are complications.

There is an important difference between the universe's cosmic time and a clock's proper time; and there is an important difference between proper time and a reference frame's coordinate time.

Most spacetimes can not have coordinate systems. Also, all physicists believe that relativity and quantum mechanics are logically inconsistent and need to be replaced by a theory of quantum gravity.

A theory of quantum gravity is likely to have radical implications for our understanding of time, such as time and space losing their discreteness and even their separate identities on the very smallest scale.

Aristotle, Leibniz, Newton, and everyone else before Einstein, believed there was a frame-independent duration between two events.

For example, if the time interval between two lightning flashes is 100 seconds on someone's accurate clock, then the interval also is 100 seconds on your accurate clock, even if you are flying by at an incredible speed.

Einstein rejected this piece of common sense in his 1905 special theory of relativity when he declared that the time interval between two events depends on the observer's reference frame.

As Einstein expressed it, "Every reference-body has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event."

Each reference frame, or reference-body, divides spacetime differently into its time part and its space part.

In 1908, the mathematician Hermann Minkowski had an original idea in metaphysics regarding space and time. He was the first person to realize that spacetime is more fundamental than time or space alone.

As he put it, "Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.

" The metaphysical assumption behind Minkowski's remark is that what is "independently real" is what does not vary from one reference frame to another. It's their "union," what we now call "spacetime," that doesn't vary.

It follows that the division of events into the past ones, the present ones, and the future ones is also not "independently real".

However, space and time are not completely equivalent even in relativity because time is a "distinguished" sub-space of the 4-d spacetime continuum.

Being distinguished implies that time isn't just another 4th dimension of physical space; it's a special dimension unlike the space dimensions, even when we confine our attention to a single reference frame.

A coordinate system is a way of representing space and time using numbers to represent spacetime points.

Science confidently assigns numbers to times because, in any reference frame, the happens-before order-relation on events is faithfully reflected in the less-than order-relation on the time numbers (dates) that we assign to events.

 In the fundamental theories such as relativity and quantum mechanics, the values of the time variable t are real numbers, not merely rational numbers.

Each number designates an instant of time, and time is a linear continuum of these instants order by the happens-before relation, similar to the mathematician's line segment that is ordered by the less-than relation.

 Therefore, if these fundamental theories are correct, physical time is one-dimensional rather than two-dimensional, and continuous rather than discrete.

These features don't require time to be linear, however, because a segment of a circle is also a linear continuum, but there is no evidence for circular time, for causal loops or worldlines that are closed curves in spacetime.


Because of quantum mechanical considerations, physicists agree that the general theory of relativity must fail for durations shorter than the Planck time, but they don't know just how it fails.

Most importantly here, there is no agreement among physicists as to whether the continuum feature of time will be adopted in the future theory of quantum gravity that will be created to take account of both gravitational and quantum phenomena. The string theory of quantum gravity predicts that time is continuous, but an alternative to string theory, loop quantum gravity, does not. (See "Atoms of time.")

Relativity theory challenges a great many of our intuitive beliefs about time. The theory is inconsistent with the common belief that the temporal order in which two events occur is independent of the observer's point of reference.

For events occurring at the same place, relativity theory implies the order is absolute (independent of the frame), but for distant events occurring close enough in time to be in each other's absolute elsewhere, event A can occur before event B in one reference frame, but after B in another frame, and simultaneously with B in yet another frame.

Science impacts our understanding of time in many other fundamental ways. Relativity theory implies there is time dilation between one frame and another. For example, the faster a clock moves, the slower it runs, relative to stationary clocks.

Time dilation shows itself when a speeding twin returns to find that his (or her) Earth-bound twin has aged more rapidly. This surprising dilation result has caused some philosophers to question the consistency of relativity theory, arguing that, if motion is relative, then from the perspective of the speeding twin, the speeding twin should, instead, be the one who aged more rapidly.

This argument is called the twins paradox. Experts now are agreed that the mistake is within the argument for the paradox, not within relativity theory. As is shown in more detail in the Supplement of Frequently Asked Questions, the argument fails to notice the radically different relationships that each twin has to the rest of the universe as a whole.

In Einstein's relativity theory, the focus is often on proper time rather than on a global, coordinate time.

Proper time along a worldline in 4-d spacetime is the time elapsed by an object having that worldline, as shown on an ideal clock having the same worldline. In the twins paradox of special relativity, one twin's proper time is very different than the other's.

There are two kinds of time dilation. Special relativity's time dilation involves speed; general relativity's involves acceleration and gravitational fields.

Two ideally synchronized clocks need not stay in synchrony if they undergo different accelerations or different gravitational forces. We've already mentioned the clock that is taken to the wine cellar.

 This gravitational time dilation would be especially apparent if one of the two clocks were to fall into a black hole.

A black hole can form when a star exhausts its nuclear fuel and contracts so compactly that the gravitational force prevents anything from escaping the hole, even light itself.

The envelope of no return surrounding the black hole is its event horizon. As a clock falls toward a black hole, time slows on approach to the event horizon, and it completely stops at the horizon (not just at the center of the hole)--relative to time on a clock that remains safely back on Earth. Every black hole brings an end to time inside itself.

If the microstructure of spacetime (near the Planck length which is much smaller than the diameter of a proton) is a quantum foam of changing curvature of spacetime with black holes forming and dissolving, then time loses its meaning at this small scale.

The philosophical implication is that time exists only when we are speaking of regions large compared to the Planck length.

General Relativity theory may have even more profound implications for time. In 1948, the logician Kurt Gödel discovered radical solutions to Einstein's equations, solutions in which there are closed timelike curves, so that as one progresses forward in time along one of these curves one arrives back at one's starting point.