You touch upon a deep issue here, as a matter of fact! It is claimed that symmetries lay at the basis of forces.The SU(2)l×SU(1)ySU(2)l×SU(1)y symmetry for the so-called unified force (splitting in the EM force and weak force after a break of symmetry, namely that of the Higgs potential) the SU(3)SU(3) symmetry for the color force, and a coordinate symmetry for general relativity. You can perform symmetry operations without truly change a system. This is simply done mentally, and by demanding symmetry, forces arise, while in fact it's the other way round. It are forces which give rise to symmetry principles. You can literally force symmetry transformations upon nature, like you do with the squares, and retrospectivelyclaim that forces are the result, but that's indeed putting the horse behind the wagon. You can rotate all points of a square locally and say that because of this forces will appear in the square to let it keep its shape (making it symmetrical wrt to local rotations or gauges), but as you say, you have to pull and push it first for these forces to appear. — AgentTangarine
On the contrary, the second notion of symmetry(17th c) from the quote you provided, ignores the location or context. The left and right are simply equal, or they mimic each other. While the first notion, which is the ancient definition of symmetry, refers to balance. This symmetry, I think, is what's dependent on location. You'll find this a lot in art composition -- paintings for example, around the 15th century.Interchangeability of the right and left, which constitutes "invariance", is only possible if the figure is considered to exist free from any context, without a location. Of course nothing really exists without a location, so "symmetry" in this sense is is just a false principle. It cannot be applied to anything real. — Metaphysician Undercover
On the contrary, the second notion of symmetry(17th c) from the quote you provided, ignores the location or context. The left and right are simply equal, or they mimic each other. While the first notion, which is the ancient definition of symmetry, refers to balance. This symmetry, I think, is what's dependent on location. You'll find this a lot in art composition -- paintings for example, around the 15th century. — Caldwell
Good topic, but out of sync, I'm afraid. — Caldwell
Nice observation. In fact, it was the attitude at the time to showcase symmetry in visual arts. So in essence, you're admiring a painting because it has symmetry (balance), but you're not supposed to notice it.And one could even take this principle further to argue that symmetry is actually a feature of the context, reducing the internal thing which is supposed to be the symmetry itself, to a simple central point within a balanced environment. — Metaphysician Undercover
This is almost similar to what I'm saying above. Symmetry becomes the object itself, and the main event becomes the background -- a supporting role to symmetry. Is this close to what you're thinking here?So the point I tried to make in the op is that the modern use of "symmetry" as it is used in pop metaphysics, in the sense of symmetry-breaking and similar concepts, derived from the application of mathematics in physics, is what we might call a perverted sense of "symmetry". It places "symmetry" as a feature of an object rather than as an arrangement of objects. We could say that it abstracts "a symmetry" as an object, from "symmetry" which is necessarily an arrangement, therefore a plurality of things. In essence, a true symmetry requires an arrangement of parts, whereas a modern symmetry is considered to be an invariant whole, thereby denying the possibility of parts. — Metaphysician Undercover
Ignore this. I get your point now. But to clarify what I meant when I posted it, I meant your OP was out of sync.I don't get you. Out of sync with what? Out of sync with the modern sense? — Metaphysician Undercover
AgentTangarine is a bot. Not a real member posting. Can we put a restraining feature on this bot? — Caldwell
The A-field in QED is caused by the electrons themselves and they induce local gauge transformations on the electron field, precisely in such a way that the Lagrangian of the conserved. The gauge changes introduced cause similar shifts in interference patterns as in the BA effect. This causes electron fields to get shifted like the interference pattern is shifted in the effect above-mentioned. The difference is that the shift is not the same everywhere (global) but rather varies from place to place. The induced local gauge transformations show themselves as interference effects (which is the only way to observe rotations of internal vectors in the complex plane). — AgentTangarine
This is almost similar to what I'm saying above. Symmetry becomes the object itself, and the main event becomes the background -- a supporting role to symmetry. Is this close to what you're thinking here? — Caldwell
Can you tell me what is meant by "the complex plane"? — Metaphysician Undercover
The issue is that a whole never really is a symmetry, so that is a misrepresentation — Metaphysician Undercover
There's a difference though but I trust mathematicians - there must've been a very good reason lateral inversion has been swept under the rug. Can you figure out why? — Agent Smith
Simplicity, I suppose. The object and the image are on opposites sides of the plane. And the reality of the turning required such that they face each other (what it really consists of), is ignored for simplicity sake — Metaphysician Undercover
n short, if there's an object, we have two lines perpendicular to each other passing through this object with their point of intersection somewhere inside that object. This framework then provides us with chirality/handedness.
When I look in the mirror, I see myself looking back at me (the reflection). Based on the above system of lines, my left becomes my image's right and my right becomes the image's left (lateral inversion). — Agent Smith
So there is a reason for the so-called lateral inversion which the mirror produces, it's due to the spatial separation between the object and the reflecting plane.. — Metaphysician Undercover
Not all the blame falls on the mirror then, huh? Suppose a line's on the line of symmetry (flush with the mirror's surface), this line, as per you, doesn't undergo lateral inversion then. However, such a line (remember only 2D objects can achieve 0 distance between itself and the mirror's surface/line of reflection) and the line of reflection/the mirror surface would be indistinguishable i.e. we're no longer talking about an object at all but the mirror itself. — Agent Smith
I don't get your point. — Metaphysician Undercover
It's all good then, no? One side of my body is actually a reflection of my other side and the mirror proves the point by lateral inversion (flipping my left and right sides) as no one (usually) reports anything amiss in our reflections. — Agent Smith
Well, try to change the left and right hands in a human body! :grin:Crucially, the parts are interchangeable with respect to the whole
I would think that a quality or attribute which is impossible for a thing to have, is a false principle. — Metaphysician Undercover
If I understand correctly, the classical "electromagnetic field" which is a property of electrons, can be represented as two distinct fields, electric field and magnetic field. I understand the electric field (E) to be spatial, representing a spatial relation to the position of the electron. The magnetic field (B) I understand as temporal, representing the changing position of the electron. If I understand you correctly, you are saying that the relationship between the E field and the B field, which ought to represent "electromagnetism", is not strictly invariant, so there is a need to introduce an A field to compensate. I would conclude that the relationship between space and time is not invariant. It is made to appear as invariant through the use of the A field. If you can explain where this interpretation is misunderstanding, or deficient, I'd be grateful. — Metaphysician Undercover
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