I have often heard or seen the word ‘symmetry’ used in physics. What does it actually mean?
This is equal to that.
Let me introduce you to Emmy Noether, and possibly one of the most profound and important ideas in physics ever.
And when it comes to the interrelation of abstract mathematical ideas and the real world perhaps one of the most clear.
It would be impossible to detail all the uses; the universe is symmetrical to an astonishing degree.
Perhaps the most common use is in the construction of physical laws in relation to space. It appears, for instance, that the laws of physics don’t change if you move one meter to the left (it doesn’t matter where “left” is). That’s a symmetry–a translation symmetry, specifically. The laws work the same if you slide in some direction, no matter how far.
There is angular symmetry. Point yourself in a different direction, and the laws work the same way.
There is also time symmetry. The laws work the same today as they did yesterday.
Some symmetries are a bit less obvious. Conservation of energy is a symmetry–the total number of joules in the universe doesn’t change. Neither does the total momentum. Interestingly, these symmetries have a deep relationship to time and translation symmetry (see Noether’s theorem that Francis Vaughan linked to).
Another type of symmetry relates to mirroring the universe across some plane. For instance, if you swapped left with right, the universe would work almost exactly the same way. If in addition you swap future with past, and positive with negative, you finally get a perfect symmetry (this is called “CPT” symmetry).
It goes deeper. Physicists have found that often there is more than one way to write your physical laws–and they don’t even need to have the same number of dimensions. It is possible, for example, to write out physical laws that only work on the surface of an object, and yet make all the same predictions as ones based on the whole volume. This is yet another type of symmetry.
There’s much, much, more. Virtually all of physics is based on the observation of one symmetry or another.
I didn’t understand all of it but I think the main message was if some change happens to an object and everything is preserved as regards it properties then it is symmetrical. So, for example, if a playing card is turned upside down, while its position has changed nothing else has, therefore, it is a symmetrical situation. Is that about right?
Thank you, that was an interesting explanation and something I will need to think about. Doesn’t this relate to speculation about new particles that may exist based on the idea of symmetry?
Seems you’re right. 
There is symmetry in the laws of physics, and there is also symmetry in individual problems. If you have a problem with symmetries in it, then the solution will also have corresponding symmetries.
For instance, suppose you have a weight hanging from the center of a room, suspended from three cables. One cable attaches to the ceiling at a point 2 m south of the center of the room, one cable attaches at a point 1 m north and 1 m east, and the last attaches at a point 1 m north and one m west, and you want to find the tensions in all of the cables. Well, the second and third cables are in symmetric positions, and so you can conclude immediately that the tensions in those cables are also symmetric. Now, I could have also set up a different problem where the cables aren’t symmetric: There’s no law of physics against that. And I could still solve that problem, but it’d be a little harder. Since I have the symmetry in the original problem, though, why not use it?
Sure, in physics, especially in quantum field theory, you can formulate a gauge theory, in which your physics is invariant under a local group of symmetries. From those constraints you can mathematically work out what particles possibly exist and how they can interact.
That could be what you heard about, especially the famous Standard Model.
Yes so this would be like a mirror image wouldn’t it? And is it conceivable that there might exist ‘symmetrical realities?’
I think so yes and I imagine they are on the lookout for these.
You can also attempt to apply concepts of symmetry to humanities.
For example “the Golden Rule”.
A physical symmetry is when you apply a transformation to some physical theory, situation, etc that leaves it unchanged. Symmetries are important in all areas of physics as they can are highly useful for proofs or generalizing arguments. Symmetries can also be a source of confusion sometimes, usually due to the distinction between different symmetries e.g.:
Continuous vs. discrete symmetries
The general symmetries of a theory vs. the symmetries of a specific situation (to which that theory is applied)
Global symmetries vs. local symmetries
etc, etc.
For example the apparent “paradoxes” of special relativity usually come about through the misapplication of symmetry.
This seems to refer to the “Twin Paradox” most obviously to me.
Can you mention one or two other well known misapplied symmetry paradoxes for me?
The Sagnac effect (probably the absolute favourite of anti-relativist cranks attempting to prove relativity wrong), barn-pole paradox.
It sounds like you’re talking about supersymmetry. Supersymmetry is a speculated extension to the current Standard Model of particle physics. It proposes a symmetry between bosons and fermions. These are names for general classes of particles (I won’t get into the details since it requires a bit more background); all particles fall into one of these two classes. Supersymmetry proposes that all particles have a “superpartner” that is similar except that it falls into the opposite class. For instance, the electron is a fermion; the super-electron would have mostly the same properties but be a boson.
Thus, the idea is that boson vs. fermion is a somewhat artificial distinction that we only observe because most particles are at such a low energy. Crank that up via particle accelerator and we may find these superpartners. The superpartners would also be present at high-energy events like the Big Bang and may explain some of the behavior there.
Supersymmetry has not yet been observed and may not be true. Physicists like it because it fixes and explains several problems with the Standard Model, such as why gravity is so much weaker than the other forces, or why it seems to break down at high energies.
Fascinating, thank you.
Some physicists like Supersymmetry. I know a couple of very eminent particle physicists who think it is bunk. It got a lot of press and lots of popular physics books have been written about the idea, but I think this is more about what is wrong with much popular physics than anything else.
Fair enough :). That said, I doubt you’ll find many avenues of physics research that don’t have detractors. GUTs, string theory, loop quantum gravity, etc.–lots of people not just calling them bunk, but saying that they damage physics as a science due to eating up students that should be working on something more productive (whatever that might be).
You mean like an entire generation of theoretical physicists dashed on the rocks of string theory? 
You see it in a lot of sciences. It is a problem with the way modern academia works.