Relativity And The Bridging To Quantum Mechanics

[Dubbelosix]

Not too long a post, but what insights do we know of in quantum mechanics that would simplify to relativity and vice versa in a natural way?

 

One example I have suggested here, is that both relativity and quantum mechanics say the same thing in regards to motion and rest: That is all systems are in motion and there is no such thing as rest. Immediately, if they conclude the same thing, then this is a bridging between the two theories - it is one but of only a few obvious connections a scientist may want to investigate in a larger picture.

 

Another one that has struck me, is that particles don't ever tend to travel in straight lines. Einstein was the first to come up with clever analogies and though experiments, seemingly connecting what appeared to be unrelated topics in physics. A good example is how he explained the analogy of being in an elevator which is falling seemed to negate the effects of gravity (in a loose way) - I say a loose way because you are still falling towards the Earth because of gravity. His simple thought experiment though, became the basis of general relativity. Only Einstein could have foresaw this theory of relativity in such a sharp way, because we learned there is a dynamic importance between the presence of matter and the effects of matter, causing a curvature of space, which Einstein interpreted as the acceleration of objects along geodesics. Indeed, anything that follows a curved trajectory, must accelerate. This is also true for the photon. If that seems strange, just remember, something doesn't need to change its velocity to actually have a measure of acceleration.

 

It is probably true that Einstein was aware of the uncertainty principle and understood it as a principle of how systems are never at rest. I wonder if it had occurred to him, that his views of relativity had an uncanny resemblance. Further, I wonder if Einstein ever pounced on the fact that particles tend not to travel in straight lines, this too, according to the rules of relativity translate into an acceleration. To manage these idea's in one go is not an easy task, because it would mean that our usual understanding of gravity has to be abandoned with. The accelerations of particles (as they travel curved geodesics) is an analogous case to the macroscopic phenomenon we have been made aware of through Einstein's amazing work. 

 

The laws of relativity even indicate that the bound trajectory of particles would imply a strong gravitational force since the same law even applies to massive bodies. Anything bound in a tight trajectory will invoke strong curvatures (or a strong gravity). There is an interpretation for gravity and we haven't completely failed to see it - Nobel prize winner Abdus Salam showed that strong force can in theory be entirely explained in terms of gravity. If it is true, that gravity plays analogous roles even on the scale of particles, then this is more in context with the idea that gravity is a pseudoforce and scale invariant - in other words, it does not just apply to the rules of massive bodies. I have a few times, raised why this idea of gravity being a pseudoforce is in fact a priori of general relativity and a fact that seems to have been lost on physicists when they extended gravity to the fields of force carriers.  

Edited July 8, 2018 by Dubbelosix

[Shustaire]

Try straight lines under polar coordinates

 

http://people.oregonstate.edu/~drayt/Courses/MTH437/2007/hw/geodesic.pdf

 

 

​ "Our first characterization of straight lines was that they do not bend, or equivalently that they do not accelerate. The standard approach to the notion of straight lines in arbitrary spaces is in fact to generalize this lack of acceleration, thus showing that the (unit) tangent vector does not change. However, this approach requires knowing how to differentiate vectors in arbitrary spaces. We choose to avoid this extra machinery, the covariant derivative, and seek a different pat

Edited July 7, 2018 by Shustaire

[Shustaire]

Here is a more advanced examination of geodesics

 

http://www.tapir.caltech.edu/~chirata/ph236/lec06.pdf

 

Please note these are lecture notes on both links.