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It is a very interesting research point to look more closely at observers in science. This becomes especially important when talking about Quantum Mechanics!

Hm, a triangle has a strict definition in euclidean space. But, the concept can also be expanded to non-euclidean space, and in fact, it is.

It is still an ongoing and extraordinary interesting problem whether space(time) itself is quantised or not! :D

So strange (:

Sure, hit me up on LinkedIn: Timo Kerremans

done@@whyofpsi

What course do you mean? :) I am always open for business inquiries ;)

Thank you, your message means a lot to me :) I am desperately looking for more time :)

That is an excellent question! Consider the case where two masses do indeed move towards each other due to the attraction of gravity. Because they accelerate towards each other, they will pick up speed. When they eventually meet, and we consider the case that they move right through each other (no collision), then they will indeed move past each other after they cross. They will move apart again, but decelerate because gravity is pulling them back in. At some point their velocity will be zero again, and they will start falling towards each other. This process will continue time and time again, each time crossing each other and then moving apart again. Now: this is exactly what happens with two meridians on a globe. They move towards each other, cross, diverge again, cross again, etc... :D

Thank you for explaining it! Only place I disagree is - why would they feel being pulled towards each other when they move apart after meeting. Since there's no absolute 'force of attraction' between them they should feel a tendency just to move away from each other which should feel like being repelled by each other. This would indeed be changed to attraction again once they reach the farthest point of curvature. The other point is, this movement must repeat endlessly, as there's no force, no creation or loss of energy within the system. Please correct me if my guesses are wrong Again, Wonderful video!

Perhaps soon ;)

We are waiting 😊

I have been super busy with other projects (and a full time job as a data scientist). One of these days my course on statistics launches, then I will have more time again and might start back into making these videos :) Thanks :D

@@whyofpsi I understand, course on statistics? Great!! But I am more eager to see your take on GRT, GWave!!

Awesome! Nature is a beauty 😎

You are very welcome! :))

I have many other things that require my focus. I made an ai-powered math and science tutor (ai-tutor.io), I'm in the process of finishing a lengthy Statistics for Data Science course. And, I have a full-time job :) But, I would love to just focus all my attention back to these kinds of videos, as they give me the most fulfilment. Thank you for your message! :)

Quite dedication! Best of luck with everything! Glad I just came cross your channel, I admire the ablility to consisely produce such high contents, thanks a lot!

Comments like this give me extra motovation to make the next video! Thanks!! 🙃

Cool, thansk for the feedback, I appreciate the honesty. In my more recent video I think this is not the case :) What did you think of the video content itself?

@@whyofpsi It was very interesting and wanted to watch it til the end but couldn't because of what I commented above. Sorry for my lack of tact. Cheers!

Whoa! I'm super curious to know from what university! It's the first time I hear this :) Was the video useful for the course material?

Actually, the answer is that events that are space-like separated, causality cannot exist as a concept. This is all special relativity. In general relativity, curved geometry does come into play. You can watch my long video if you want to learn more about it.

:D !!

What do you mean?

@whyofpsi a and b are not in causality to begin with. You just are writing nonsense

To be precise, the concept of simultaneity (things happening at the same moment in time) because relative! In this particular case, events A and B are outside each other's light-cone: they can never influence each other.

You are very welcome! I'm super glad I was able to convey the message :))

I agree with you on the first part, they are indeed not causally connected. I might disagree with you on the second statement. You could argue that general relativity as a theory for Gravity is flawed in the sense that it has a limited region of applicability: it doesn't work within a quantum framework. Special Relativity is a very concise framework that works very well within its bounds, and its bounds a very precisely known.

Thank you! I use Manim, which is a Python Library. It has a very nice and helpful community.

@@whyofpsi Thanks for the reply! I'll check it out

How would you explain the countless of experimental evidence in support of relativity? Remember: science is about testing theories against real world observations, not a mere thinking exercise.

​@@whyofpsiname one experiment. Just one that proves time-dilation.

@@stewiesaidthat They have flown very accurate clocks around the Earth, and compared their times with initially synchronised clocks that remained on the surface. They were not synchronised when compared.

@@whyofpsi do you not understand what it is that clocks are measuring? Do you think that rulers measure inches? Or thermometers measure degrees. Or that scales measure pounds?

@@stewiesaidthat you have no knowledge of even basic physics. Scales indeed measure pounds, i.e, weight, which is a force, and not the same as mass. Rulers indeed measure inches, since an inch is a measurement of distance, in the same way as miles, or metres. Clocks measure units of time, e.g. seconds, minutes, etc. Those are units that we are comfortable with, to aid our daily lives. Time in relativity theories is an intrinsic property of the universe. It is not governed by any Earth based units of measurement. Time is indeed "malleable", it can change its value, depending on speed of travel, or the strength of a gravitational field. This has been proven multiple times by numerous different experiments. If you can't accept that then that's your problem, but don't pretend you are right, based on your own extremely limited knowledge.

I'm glad to hear the video helped you. Of course, 60 seconds is not nearly enough! I don't know about books specifically, sorry. RUclips also provides good practice, if the videos are long and in depth. If you need example exercises, you can see if there's any helpful videos on my other channel: Pen and Paper Science. There, I even have a more in depth and long video about Lagrangian mechanics. Good luck!

I recommend you "mechanics vol 1" frok Landau-lifshitz, the "classical mechanic" from john r taylor and the goldstein "classical mechanic"

​@@claudio6947thanks 👍🏻

I am not aware of that. So many independent observations concur with an expanding universe.

Well, the concept of spacetime has been tested time and time again. In fact, it was necessary to explain phenomena we observed. Likewise for the curvature of spacetime.

​@@whyofpsithere is no spacetime except in Einstein’s fantasy universe. It's space and time. Teo separate frames of reference. Newton's F=ma deals with motion in space and E=mc deals with time aka radioactive decay. Acceleration in space = acceleration in time. Unless a counter force is applied. Like cryostasis and other such cooling systems. I can tell you for a fact that Newton's gravity and Einstein’s relativity is 180 degrees opposite of reality. That's why you can't see the glaring error. Take the falling apple. Turn the frame horizontally and replace the tree with a truck and the ground with a trailing vehicle. The apple falls from the truck and impacts the trailing vehicle. How do you describe that? Gravity? Was the apple attracted to the trailing vehicle on account of its mass? What if that was a motorcycle. How about a pedestrian and the truck was going around a curve. Gravity is not a pulling force. It's a pushing force. The resistance of mass to being accelerated. The laws of physics are equally valid in all frames of reference. That negates special relativity. Mass by itself has no force. That negates general relativity and Newton's gravitational attraction. Gravity doesn't explain the Earth's tides but acceleration does. Relativity is flat earth science. Just turn the frame 180 degrees and you will see reality.

@@whyofpsi A thought experiment does not prove anything in the real world. What tests are you referring to ? First SPACE and TIME are not the same thing. I don't care who said it. SPACE is NOT A CURVABLE FABRIC LIKE SUBSTANCE. Space is the absence of MATTER space is the Near NOTHING between things/matter. NOTHING is uncarvable AGAIN I don't care who said it. and Yes I know the 'theory' but I don't agree with it and I've not seen it in real life. Light can curve passing through a corona but GPS DO NOT USE Einstein's theory of spacetime to operate.

Thank you, it means a lot to me (: Yes, that would be unimaginably unlikely :D

Yes it is, I do cover enough to get a good grasp on what curvature means, both intuitively and mathematically. My video on Time is shorter :)

@@whyofpsi Space means empty space in 3 dimensions.... rest all (matter, speed time, distance traveled in space) are relative to each other...! Appreciate your efforts to explain things mathematically.....But I don't think empty space actually curves! The concept of space is flat or curved is mixed up...! Liked your time video...!

On a flat surface, the shortest distance between two points is a straight line. On a sphere, of course, what does it mean to be a straight line? The generalisation of a straight line on curved surfaces is called a geodesic, and for a sphere that would be a meridian. (:

It is related to defining the curvature of a surface, which in turn is important for physics in the theory of Gravity: General Relativity! You can watch my full video on curvature to learn more! :D

Thanks! It's quite difficult to make something under 60 seconds that is still meaningful 🙃

One of the central tenets of General Relativity is indeed that Gravity can be described not as a force, but as the curvature of space-time. This curvature is exemplified by non-straight geodesics. And since objects, in the absence of any external force, follow geodesics, they will indeed follow curved trajectories.

Gravity does result in accelerating objects with mass, yes. What causes dilation and contraction of space (and time), is the relative motion between different observers. For these effects acceleration is not even needed, only relative motion. But, as you say, they also occur for acceleration. Because Gravity the effect of gravity cannot be distinguished from acceleration (locally), these effects indeed occur in gravitational fields, as you mention with the example of signals from satellites. However, as Special Relativity teaches us, relative motion (and thus gravitation/ acceleration) makes it so space and time cannot be considered separately, they have to be described simultaneously as space-time. Therefore, the warping (contraction/ dilation) happens in space and time together.

​@@whyofpsiI don't understand how people can be so dumb. Space and Time are two separate frames. Gravity has been proven to be an effect of acceleration. Do you know what anti-gravity is? Accelerating yourself. Riding a motorcycle, you are one with the machine. You feel no acceleration at your back. Now lean back into the seat back. You feel gravity because the bike is now accelerating you. You feel gravity at your feet because the earth is rotating on its axis. Accelerating you out from the center and also forward. That's your curved space. You are fooling yourself with the curved space triangle because the 3 points are in different planes. A triangle on a sphere is different than one on the cylinder because its 3 sides are longer. Rotate your cylinder 90 degrees and then draw your triangles. When you don't understand the physics, the mathematics blinds you to the errors. The laws of physics are equally valid in all frames of reference. Vertical. Horizontal. Curved.

Exactly! That's why you could say that causality can be broken, but only for cases when it doesn't matter 🙃

@@whyofpsi ❤️

@@whyofpsidoesn’t matter ie. wouldn’t change the outcome of it was broken?

​@@ebk7073344yes

This is exactly why causality is not a force. It's all correlative, aka inductive. So the reason you can't break causality, is because it's simply an assumption, and not real in of itself.

That is indeed the case :) The surface of a cylinder is not intrinsically curved! :D

The components of a vector are indeed coordinate system dependent. If that's what you're asking? :)

@@whyofpsi how to espress sum of two vectors, u and v, directly by polar versor when u and v do not have the same origin ?

@@glcpit7797 First, you transform the vectors from cartesian coordinates to polar coordinates. This is as simple as doing matrix multiplication with the well known transformation matrices. Then, you would want to shift both vectors to the origin, which is vector addition. Then, you add them together by adding the corresponding components together. This is technical, and something I cover on my other channel: "Pen and Paper Science"

We need to think about what it means to "prove" something in science. Science is not mathematics: we can never definitively prove something. What we can do is explain observations using theories. In this regard, there are several observations we made, such as gravitational lensing, that are hard to explain without the curvature of space-time.

​@@whyofpsigravitational lensing is easy to explain. Rotating objects create an electromagnetic force field that electromagnetic waves interact with. Haven't you've heard of the Earth's magneto sphere. I suppose that's caused by your notion of 'gravity'.

@@stewiesaidthat If it were rotating, charged objects interfering with the electromagnetic waves (light) from the object, then the bending would be asymmetric, which it is not.

@whyofpsi light travels in its own frame of reference. Independent of the source and observer. I don't know what they are teaching you in school, but this is one of the first things that is usually taught about electromagnetic waves.

So how does that relate to anything I said ?@@stewiesaidthat