3D Gibbs vector calculus may live on in math, but as a physics tool it has perhaps too many defficencies to go beyond freshman level in college, and seems less and less used. In research, the same applies, for the last 150 years, to the three Newton's laws [1].
For example, compared to Euler angles in 3D, 4D vectors such as quaternions are simpler to compose and avoid the problem of gimbal lock. Quaternions have applications in computer graphics, computer vision, robotics, navigation, molecular dynamics, flight dynamics] orbital mechanics of satellites and crystallographic texture analysis.
But quaternions also have representation defficencies. Rather than following the conventional ways out of the Gibbs system, such as Geometric Algebra or Quaternion Algebra, physics has been using, instead, analytical methods such as of Lagrange and Hamilton to describe equations of motion in physical systems, without vectors or forces. Then, it seems from usage that, while the use of vector systems is a choice in mathematics, physics has not been attempting to use vectors to calculate reality -- although it can be used with the public, in explaining a limited part of reality.
Comment: We live in a 4D world of three dimensions of space and one of time, where relativistic effects play a daily role, e.g., in GPS, your towel, your body, and anywhere with electrons! Special relativity does not start to have effects when an object (your car, for example) moves after 0.1c, the speed of light divided by ten, as some not so careful people might think. Movement is relative and electrons in a magnet on your car have electrons moving near c, and that electric charge creates a magnetic field, so that the are is actually no magnetic filed per se, E and B are an illusion created by moving near c, relatively, in 4D. So, competitively, students should not learn what they cannot use, or use poorly.
Therefore, as part of this change, physics students may soon not use 3D vector calculus or Newton's laws in physics anymore, even in what used to be called 3D reality, but mathematics may, as cited [1], being always a fair game in maths. In research, 3D vector calculus and Newton's laws seem to be NOT publishable, even in maths it seems to be rather non sequitur.
DISCLAIMER: This question is quantitative, and justified, part of a research project. Opinions are off-topic but welcome and can be added to the project itself, as a comment.
[1] https://www.researchgate.net/post/Is_Newtons_Third_Law_a_misconception_A_metaphysical_dogma
Ed, you keep calling for an end to the most commonly used tools and techniques, just because they might not apply under certain conditions. I don't buy it. As long as people are designing and building things for conditions that the very vast majority of people live under, or come now, make that everybody, 3D vector space and classical physics will exist, and will be used every single day.
RGB plus white (RGBW) has little to do with this. Math has no problem creating multi-dimensional spaces, even way beyond 4D. Hyperplanes and hypersheres of any number of dimensions are common pratice in linear programming, for example, when objective functions have more than just 3 or 4 variables. Which is hardly unusual. But this does not negate the fact that physical objects around us are extremely well described using 3D graphics and classical physics.
Of course, you can't expect original research in physics today to consider only classical physics.
I did some numbers for you, to illustrate that the difference between classical physics and relativity, in our practical reality, even if we were to somehow travel at the "enormous" speeds of Voyager 1. These differences are minuscule. They would not change the way we design most things for daily use. And yes, the effects are significant enough that the GPS design took them into consideration, when calculating time, but even having done so, how do you think position is computed? Same old 3D vector space!
Hello Albert,
If you do not have access to answer the question, please do not answer what you like.
Your answer above is off-topic, and you keep defending that 3D describes physical reality, when now, for more than 100 years, we know we have at least three dimensions of space and one of time, and effects are not just a matter of speed; but that is what not careful people may think.
Time is not absolute, and this matters in research and daily life. Your employer certainly does not design airplanes in 3D, ask about the gimbal effect.
Cheers, Ed Gerck
Hello Farid,
Your answer is off-topic, the answer is quantitative, a number. If you don't have access to it, don't answer what is not relevant. This the second time I see this behavior with you, trying to generate traffic, one could think. This is not a reply, but a kind request to stop behaviour that is not called for.
Cheers, Ed Gerck
Hello Farid,
This not your question, and you do not decide what is on topic here. Please do not reply to this note, this is notice of non-compliance for your posting.
If you want to contribute, productively, you are welcome to add your note on the project. I hope it is useful, and the questions are better explained in the project. We can explain further, and thank you if you want to contribute.
Cheers, Ed Gerck
Dear Farid,
I went to your home page in RG and I see you have been undervalued. I suggest you change your statement, to a positive view of time used, everything in life is beautiful and useful! I am sure you grew in this process. The words, I am sure also, does not reveal your true nature. Please delete your postings above, for better karma, and I will delete mine, including this one. This an honest offer, for a better restart.
Of course, I am not a Nazi, and even saying that tell my Jewish and Muslim friends that one still needs to watch words. In some countries, and for a friend who was in a concentration camp during 4 years, it is not a joke, believe me, she suffered more than you and I combined, and she was always happy. Trust yourself!
Cheers, Ed Gerck
Hello Farid,
All is well, and already solved. Please do not reply except to the question asked here, a number, of how many physics articles do you see that were published in top journals, that use 3D vector calculus or Newton's laws, in last 10 years?
Usage seems to be close to zero in research. Maybe an opportunity?
Cheers, Ed Gerck
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