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.
<ul>
<li>Einstein realized that the speed of light - a speed that stayed constant - was a measurable manifestation of the symmetrical relationship between electric and magnetic fields.</li>
<li>Light didn’t need anything to travel through because it was itself electromagnetic fields in motion.</li>
<li>There was no universal here and now.</li>
<li>It took some years for Einstein to acknowledge that space and time are interwoven and impossible to disentangle.</li>
</ul>

Einstein and Light

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 four-dimensional world with gravity.
Certain dualities suggest that space-time emerges from something more basic, what Einstein called the "spooky" connection between entangled quantum particles.

Dualities

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 description of nature. But symmetry has not been able to explain why gravity is so weak or vacuum energy is so small. The idea of symmetry may be very powerful, but we may have to give up on these principles that have worked so well.

Symmetry

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 antimatter - a symmetry. Yet if the energy of the Big Bang created both matter and antimatter equally, they should have destroyed each other, leaving nothing behind.

Broken Symmetries

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 road ahead.

Insights of Albert Einstein

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. "The speed of light can't remain constant if space-time is crumbling," says physicist Stephon Alexander.

Not giving up on symmetry

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 energy, the energy-matter content of the universe never changes. Matter and energy are less fundamental than the underlying relationship between them.

Some changes don't change anything

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 the state of motion. This leads to effects known as "space contraction" and "time dilation."
As you work at your desk, you move through time, but not through space. A cosmic ray moves over vast distances at nearly the speed of light but takes little time.

Unified space-time

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.

Relationships over things

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 describe the internal structure of the system of particles in our world. Physicists can move, rotate and distort their equations without changing anything important. The result is a look at the hidden structures that supports the basic ingredients of nature.

Gauge symmetry

After Einstein, the pull of symmetry became more powerful.
<ul>
<li>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."</li>
<li>Wolfgang Pauli, trying to account for the energy that seemed to go missing during the disintegration of radioactive particles, discovered that the missing energy was carried away by a particle, known now as the neutrino.</li>
</ul>

Matter

Einstein's special theory of relativity applies only to steady, unchanging motion through space-time, not accelerating motion like an object falling toward Earth.
<ul>
<li>It troubled Einstein that his theory didn't include gravity, and his battle to incorporate it made symmetry central to his thinking.</li>
<li>Einstein later understood that gravity is the curvature of space-time itself. Falling objects follow the space-time path carved out for them.</li>
<li>After general relativity was published, it appeared that energy might not be conserved in strongly curved space-time. But mathematician Emmy Noether proved that the amount of energy (including mass), the amount of electric charge, the amount of momentum, are all associated with a particular symmetry, a change that doesn't change anything.</li>
<li>Noether showed that the symmetries of general relativity ensure that energy is always conserved.</li>
</ul>

Gravity

Lurking behind Einstein’s theory of gravity and our modern understanding of particle physics is the deceptively simple idea of symmetry. But physicists are

Matter

Similar ideas to Matter

Dualities

A Quantum Transformation

Erwin Schrödinger proposed a paradox