Many insights of Albert Einstein are now part of popular imagination: black holes, time warps, and wormholes show up in movies and books.

Less famous, but probably the most revolutionary part of Einstein's phenomena, is a simple idea that shows how pieces fit together and illuminate the ro...

The most fundamental aspects of nature stay the same.

For example, Einstein's papers on relativity show that the relationship between energy and mass is invariant, even though energy and mass can take on many different forms.

Even though matter produces ene...

We often think of things as the heart of reality. But most often the relationship is more important, not the stuff.

We may think "stuff" like space and time are unchangeable aspects of nature. In reality, the relationship between space and time stays the same.

The relationship that mattered most to Einstein's ideas was symmetry. Scientists describe symmetry as changes that don't really change anything. More complicated symmetries have led to the discoveries from neutrinos to quarks.

Symmetry is at the root of our descrip...

Albert Einstein did not think about symmetry when he wrote his first relativity papers in 1905. He was considering several seemingly unrelated puzzles and connecting the dots.

• Einstein realized that the speed of light - a speed that stayed constant - was a measurable manifestation of...

Unified space-time starts to make sense if we think that the speed of light is a relationship between the distance traveled over time.

Because the speed of light can't change, your laser beam won't go any faster. The measurement of distance and time must be changed instead, depending on th...

Einstein's special theory of relativity applies only to steady, unchanging motion through space-time, not accelerating motion like an object falling toward Earth.

• It troubled Einstein that his theory didn't include gravity, and his battle to incorporate it made symmetry central to hi...

After Einstein, the pull of symmetry became more powerful.

• Paul Dirac, trying to make quantum mechanics compatible with the symmetry requirements of special relativity, found a minus sign in an equation, suggesting the existence of "antimatter."
• Wolfgang Pauli, trying to acc...

From the 1950s, invariances took on a life of their own. New symmetries, known as "gauge" invariances, became productive by requiring the existence of everything from W and Z bosons to gluons.

Gauge symmetry dictates what other ingredients you have to introduce. Gauge symmetries d...

Symmetry, as it is understood, seems not to answer the biggest questions in physics. In some cases, symmetries show the underlying laws of nature that do not show up in reality.

For example, when energy congeals into matter (E = mc2), the result is an equal amount of matter and antimat...

Duality is a closely related idea to symmetry. Wave-particle duality has been around since the beginning of quantum mechanics. But newfound dualities have shown interesting relationships. For example, a three-dimensional world without gravity can be mathematically equivalent to a fou...

The idea of symmetry proved very powerful. Giving it up would mean giving up on naturalness - the idea that the universe has to be exactly the way it is for a reason.

But inside black holes, the speed of light (which grounded Einstein's work) will not play a vital role in the future....