In this article, I want us to discuss a special topic in physics, and which is very important for our resolution of the crisis in physics. This topic is about what I have personally chosen to call the law of unity.
The law of unity is not something new; it is what Einstein referred to as the principle of general covariance in his general theory of relativity. But I most times fancifully refer to it as the law of unity.
So, what is this law of unity, which is also Einstein’s covariance principle? Simple, the law of unity is what states that the laws of physics are the same for all reference frames, both uniform and accelerated frames.
Recently, I just can’t take my mind off this law. When I take my bath, I think of this law. When I am strolling on the street, I think of this law. When I am even in a discussion with someone, I still think of this law, and even when I am alone on my bed, the law comes to my mind as the laws of physics are the same for all reference frames.
With how often I think or remember this law these days, it is beginning to feel as though the universe is communicating with me, which is what it really is.
This law or statement is the most beautiful and apt statement of cosmic unity. To understand this principle and its deepest implications is the noble of task of physics, and this is why I have decided to write this article.
This is so that you too can have your day filled with the most profound thought of the law of unity (or the principle of general covariance). And as we do this, we would align our mental vibrations together creating the right environment for the second scientific revolution.
When we look around the world and even to the far distances of the universe, we see unity, we see the law of unity. The natural unity which we easily observe in the universe is a testament of the law of unity, which is that the laws of physics are the same for all reference frames.
So, the noble task of physics is to capture this law in theory, and to remember that Einstein attempted to do this in general relativity raises the question, why didn’t we have the unified theory then?
Any theory based on the law of unity is supposed to be the final theory that describes all things, both the atomic world and the non-atomic world. But as we all know, Einstein’s general relativity theory failed in this regard.
Listen, there is no other deeper or fundamental law like the law of unity. Any theory founded on it is supposed to be complete and penetrating even into the nature of the atomic world, which general relativity failed to accomplish.
I want to state unequivocally that I appreciate Einstein’s theory of relativity. I really do, especially as this theory introduced us to the weak and the strong equivalence principles.
However, the theory failed in its core purpose to reflect the law of unity or that the laws of physics are the same for all reference frames.
The theory did not capture this truth because if it did, it would have unified physics and also come around to explain quantum mechanics in an insightful way.
I sometimes think that this must have bothered Einstein himself because he was very concerned about the fundamental problems of physics more than all his contemporaries.
After general relativity, he went ahead to search for the unified field theory. But in hindsight, we see that he had missed his step already. His principle of general covariance was all that was needed to explain all the domains of physics.
A good look at the principle shows its potential depth and fundamental generality, and in fact, general relativity would have been the unified field theory and not the one he later pursued.
The law of unity is the most naturally assertible law in physics. In fact, recently, I say it to myself a lot and aloud, especially when no one is around. I will just say, “the laws of physics are the same for all reference frames.”
Try it yourself right now, just say it with the conviction of the unity of the universe and see how it feels.
But this law has been with us since Einstein, but what happened is that we failed to capture the scientific or theoretical meaning of this law.
Einstein in special relativity had begun with a special or an approximate version of the law of unity, which is that the laws of physics are the same for all inertial reference frames. This was the Lorentz invariant principle for uniform or inertial reference frames.
But he went ahead to extend this principle to apply to accelerated frames, and he then informed us of the principle of covariance, which is that the laws of physics are the same for all reference frames.
But a closer look at the new theory, that is general relativity, showed a marked geometrical deviation from special relativity. That is, while in special relativity we dealt with Euclidean space-time geometry, in general relativity, we dealt with a curved Riemannian space-time geometry.
But Einstein was able to make it such that the curved geometry reduces to a flat one when we transit to uniform frames. While this is an applaudable achievement, we still have to ask ourselves if this is the proper representation of the law of unity.
This is because post-modern physics or would I rather say, absolute relativity, is giving us a different view of the law of unity or of the principle of general covariance.
Absolute relativity is informing us that for the law of unity or the principle of general covariance to be true and rightly represented all reference frames, both uniform and accelerated, have to be based on Euclidean space-time.
This is the only true manner in which we can see that the laws of physics are the same for all reference frames. All reference frames must be based on a unified geometry.
This is important. It cannot be that uniform frames are based on one geometry while accelerated frames are based on another geometry and that the latter geometry can be reduced to the former.
According to the law of unity, the Euclidean space-time is the geometry of all reference frames. This is beautiful! Our natural sense of the unity of the universe must be because of the single unified flat geometrical space-time of the universe.According to the law of unity, the Euclidean space-time is the geometry of all reference frames.Click To Tweet
Thus, whether you are looking at uniform frames or accelerated frames or at the atomic world or at the non-atomic world, you are looking at one single space-time geometry.
This is the noble task of physics, to adequately represent this truth for us to see. And in this regard, general relativity being a geometrical deviation from special relativity did not accomplish this.
The law of unity which states that the laws of physics are the same for all reference frames is what a theory of motion based on only the flat space-time can represent.
And in an amusing way, I sometimes see the law of unity as the inkling of God. I sometimes imagine myself meeting God, and asking Him what the fundamental law of the universe is?
And then, He would just say to me: the laws of physics are the same for all reference frames. Afterwhich, He would now leave me to figure out what it means. At this point, I will just be racking your brain for what that means.
I imagine this scenario in my head most of the time, and it so feels like what would really happen if that be the case.
But today, I want you to begin to have a glimpse of what the law of unity implies for physics. It implies that all frames and domains – that is referring to the atomic and non-atomic domains – are based on a single flat space-time geometry.
And in fact, another way that the law of unity can be stated is that the space-time geometry is the same for all reference frames. This is because at its base, the law of unity is a statement of unified geometry.
And this unified geometry of the universe implies that the same mathematical framework holds for all reference frames. This is the true meaning of the mathematical unity of the universe which physics had failed to accomplish, and which physicists did not pay attention to until today.
The noble task of physics today is to push the law of unity to its farthest limit and be convinced that different frames must have the same space-time geometry and not that one geometry of a frame can reduce to the geometry of the other as the case has been.
And it is because of this our failure to capture the true essence of the law of unity that physics fell into the unification crisis. We couldn’t bring atomic and non-atomic physics under one unified picture because we had broken the law of unity.
But now, we have the right representation of the law of unity in front of us, and it is now our noble task as physicists to understand and to honour the meaning of this law as it must be represented in our theories and theoretical exploration of the universe.
Until next time,
I will be here.
– M. V. Echa