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Robin04
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What would the world look like if there was no translational symmetry? How would certain laws be different and what wouldn't change?
Momentum would not be conserved. Other than that, I don’t think more can be said without specific details about how the symmetry was brokenRobin04 said:What would the world look like if there was no translational symmetry? How would certain laws be different and what wouldn't change?
And in what ways could the symmetry be broken? I know that this is not about "real" physics, rather about fantasy, but I just saw a lecture online where the teacher talked about symmetries and he said that we could imagine a world where certain symmetries could be broken, and this really made me curious. I suspect there is an infinite number of ways these alternative worlds could be imagined, but I'm just wondering how our univserse would look like if some laws of physics were different (without being exhaustive).Dale said:Momentum would not be conserved. Other than that, I don’t think more can be said without specific details about how the symmetry was broken
Basically, translational symmetry means that the Lagrangian is not a function of position. Any Lagrangian which is a function of position would break translational symmetry. So the ways that the symmetry could be broken are every way you could make the Lagrangian a function of position.Robin04 said:And in what ways could the symmetry be broken?
Oh, I missed responding to this earlier. If there were a center and if the universe were isotropic then you would have some sort of central potential. Instead of force-free objects traveling in a straight line at constant speed they would spontaneously accelerate towards or away from the central point.Robin04 said:So if space did have a center, how would that affect the conservation of momentum and the rest of physics?
Would it be a good example if gravity depended on the position? Like let's say the gravitational constant is actually not a constant. It would be fun to calculate this.Dale said:Oh, I missed responding to this earlier. If there were a center and if the universe were isotropic then you would have some sort of central potential. Instead of force-free objects traveling in a straight line at constant speed they would spontaneously accelerate towards or away from the central point.
Generally to have a physical effect what must change is a dimensionless constant. If only dimensionful constants change then all you are doing is changing your units.Robin04 said:Like let's say the gravitational constant is actually not a constant.
I don't really understand the difference in physical effect between the two options. Could you explain it more precisely, please?Dale said:Generally to have a physical effect what must change is a dimensionless constant. If only dimensionful constants change then all you are doing is changing your units.
Here is a good article by John Baez describing the difference:Robin04 said:I don't really understand the difference in physical effect between the two options. Could you explain it more precisely, please?
Translational symmetry refers to the property of a system or object in which it remains unchanged under translation, or movement along a specific direction or axis. This means that the system or object has the same properties or characteristics at every point along the translation axis.
Translational symmetry has a significant impact on laws and the world around us. Many laws and principles in physics, such as the laws of conservation of energy and momentum, rely on the existence of translational symmetry. It also plays a crucial role in the development of technologies and our understanding of the natural world.
Some common examples of translational symmetry include the repeating patterns in wallpaper, the arrangement of atoms in a crystal lattice, and the motion of planets around the sun. In each of these cases, the system remains unchanged under translation, either in physical space or in time.
Translational symmetry is just one type of symmetry, along with rotational symmetry, reflection symmetry, and scale symmetry. The main difference between translational symmetry and other types of symmetry is that it involves a specific direction or axis of translation, while other types of symmetry may involve rotations, reflections, or scaling in any direction.
Yes, translational symmetry can be broken in various ways. For example, an object may lose translational symmetry if it is subjected to external forces or if it is damaged. In certain systems, translational symmetry may also be broken spontaneously, leading to interesting phenomena such as charge density waves or superconductivity.