The first half of your video is pointless since Norton himself constrained the domain to where the ball doesn't leave the surface of the dome. I read his paper a few years ago. Second, I used to also think the jerk/snap discontinuity was a problem (making the situation unphysical) but that's not true. If you concede that a ball launched upwards with a certain exact energy will roll to a stop at the apex and stay there balanced, and you assume time-symmetry, then it necessarily follows that Norton's Dome is valid and sound and physical. The balanced ball *will* eventually fall and roll down. The only issue is that it would take infinitely long to do so. But it's irrelevant since Newtonian systems capable of balancing balls on points don't experience time. Time begins when the ball starts rolling. One more thing that will help you: just use a hemisphere dome.

I'm so happy someone smarter than I was able to explain the issue with this dome. I could only explain the issue using the definitions of the words used in the presentation.

I gave a thumbs up, but I disagree. Only the third point is really relevant. My issues: 1. The higher derivatives are not part of Newton's axioms. So if you need to change it to include higher derivatives, Newtonian mechanics is admittedly incomplete (like Norton's dome shows). 2. I see no physical reason for snap or jerk to exist in general. Nor a reason for them to be continuous. 3. You can make a different dome with the same behaviour but, where all higher derivatives in time for both trajectories exist and are zero at the excitation time. Essentially you have to force exp(-1/t²) for t>0 to be a solution. Similarly to Norton's dome you can work backwards to get the desired shape.

Awesome video! The visualization at 4:58 really helps in understanding the concept. It feels like relativity is finally starting to make sense to me.

Oh my gosh, your video is so well put together. Your channel will definitely grow

Here at 67 subscribers for when you make it big! Keep up the good work, very entertaining methods of explaining your points

I watch a pretty decent amount of science KZbin and yours is the first video I’ve seen that visually explains a Lorentz transformation. I always had to just gloss over that part of any relativity explanation and now it seems perfectly clear. Thank you!

Also, as you increase your velocity, it will take increasingly more energy to keep increasing your velocity, to the point where it takes infinite energy to reach light speed. This happens because your mass actually increases as you speed up (a tested and proven fact)! The only exception to this is something that doesn't weigh anything... Like a photon. This is why photons can travel at the speed of light, but curiously, they never experience time themselves!

@BAM# Subscribed!!

1:09 "Alice fires his ingines and accelerate..." It's the end of the Special relativity and inertial frames right there. Your "revolutionary" statement that "acceleration is relative" doesn't surprise me. You introduce new physic and it's your right, but don't claim to explain anything with old rules when you invented yours "special".

Amazing.... ❤❤❤

1:11 IMHO "we" can only "travel", I mean we can only be, along the "t" axis, that's the whole point of a rest frame. All the other lines represent the trajectories of other objects traveling at a constant speed (otherwise the paths would be curves) and starting from "our" same position (otherwise they would not start from the origin) as seen by (that is relative to) "our" reference frame. When you make a LT you are changing "our" speed (the speed of the observer) to match that of the other objects so that you can end up with one of those objects' rest frame, and doing so, you are not in "our" previous rest frame anymore, that is you are not "we" anymore, that is you/we are one of those objects. 3:13 Here you don't have a single space-time diagram anymore. Here you have the sovrapposition of 2 diagrams. If you decide that the orthogonal one is "your" diagram, then the other doesn't show you (you can't be at 2 places at the same time), if you decide that the "sheared" diagram is the one showing your "events" then the orthogonal one is that of someone else. 5:21 The lightcone is not about "seeing", it is about speed and positions of objects relative to us, that is relative to our origin's position and relative to our origin's instant, and that are faster than c. It doesn't say anything about "visibility". 6:28 I'm sorry but were you talking about a space-time diagran or a space-proper_time diagram? A space-proper_time diagram would be one in which the vertical axis values "depends" on the horizontal axis values, that is they wouldn't represent independent variables. Does that would make any sense? It would be like having positions/distances on the horizontal axis and, say, velocities in the vertical axis, in such a diagram you could draw self-intersecting curves and time, that is still present in velocities, wouldn't be represented in an explicit way, you wouldn't know when a certain change in position or velocity had happened. If it is a "space-proper_time" diagram because in the vertical axis we have "ct" then it is not proper-time in a proper way.

7:07 "Alice's 1st frame" !!?? Are you really saying that Alice "has more then one frame"?? What does that even mean? 13:15 Same here, what you are drawing here is a weird diagram, one that is only *partially* that of Alice and then is that of someone else, but who?. In a spacetime diagram relative to e.g. Alice, his position (or better: *distance* ) coordinate must always be 0.

So is NOT acceleration that is absolute, is NOT force that is absolute, is NOT an inertial frame that is absolute, what is absolute is geometry !?. You are saying that there IS an absolute thing, and that this ABSOLUTE thing is the chosen abstract mathematical construct. Is it really this what you are saying?

Great great video, I really liked it... 🙂🙂🙂 "It's not the acceleration or the force or the inertial frame that breaks the symmetry. It's the PATH!" : You're right !!! I believe that the twin on Earth is younger, if we consider the motion of the Earth in the frame of the spaceship. (round trip) And this is not a defeat, the motion of the spaceship (in the frame of the Earth) is different from the motion of the Earth. (in the frame of the spaceship)

More garbage from the Church of Relativity. What does it take for you kids to understand that Einstein’s Relativity is mathematical nonsense? The properties of light make it an absolute reference marker in which to measure ALL other motion against. Space and Time are SEPARATE frames of reference. By combining the two, you show just how ignorant you are. Keep playing in your sandbox because you are not intelligent enough to run with the men. 1) as previously stated, Space and Time are separate frames of reference. 2) Clocks are instruments that measure motion in space expressed in units of Time. No different than rulers measuring length expressed in inches. 3) Clocks in motion use the SAME amount of energy as stationary clocks. E=mc where c is the speed of light. Speed is distance/Time so Energy equals Time. Both clocks used the same amount of Energy so experiencing the same amount of time. 4) the laws of physics are equally applicable in ALL frames of reference. If Force equals Acceleration in the Space frame, then Force equals Acceleration in the Time frame. The twin undergoing acceleration in space is also undergoing acceleration in time unless they are experiencing a zero gravity (low acceleration) environment. The only reason there is a paradox is because some dufus combined the two frames and declared that clocks measure time. They dont. Based on the limited information given, the clock readouts, the only conclusion that is valid is that both twins are the same age. One just experienced more space as measured by the onboard instrument that strictly measures motion in space. The clock's cesium-133 atom is being chilled to absolute zero to prevent an acceleration in time event from occurring. Unless the observer is also in cryostasis, they aren't even in the same time frame as the clock. If you want to get really technical, the traveling twin most likely has a shorter lifespan since they experienced more g-forces.

I could almost understand but it's still over my head. I understand time slices and how the faster you travel in a certain direction the more of the future of that direction of the universe becomes a causally related part of your factual present tense sense of now. While the past (for a person who is not changing his distances from the other relative objects in the vast universe, ie staying still) of the other direction becomes his present tense. But I didn't notice any mention in the 2 times I watched this video of the gravitational effect of the acceleration. So I can't help but think acceleration is not relative. I we imagined the whole universe was doing the acceleration (ofc it's not though bc the thrust is coming from the rocket and isn't being applied to the universe) and we were sitting still with an inert frame of reference then where do the g forces come from? Maybe another video explaining how g forces exist if all reference frames are to be considered equally valid.

All was well until the claim that a space time position is the same as spacetime coordinate 😅 (paraphrased at roughly 16:50) Coordinates are frame/chart dependent, position is not. But great video! 😊 Maybe this is making it slightly more complicated than it needs to be though. Just showing the picture of the three lines and Lorentz-transforming that picture is enough to show that that does not move the kink from Alice’s curve to bobs. So the situation is not symmetric. That’s it. The rest of that is measuring the proper time of each curve. (Clocks don’t have to emit any significant light-signals to count time locally, so that part of the argument is unnecessary, though it is somewhat illuminating as well). A lot of the crux is to understand the prerequisites about what a spacetime diagram means in the first place. But that is more about stating the rules of special relativity (or whatever setting is preferred) and how to work with it. I think plenty of the confusion people have about this topic starts with the basics. Once they have the basic background, the resolution of this paradox is pretty much conveyed by just drawing the pictures. In more general cases it might be hard to draw pictures and then you might need to do the calculations, but here it just happens to be just enough in my opinion.

This is NOT the twin paradox!!! The paradox is that while the moving twin is moving and the moving twin looks back at the at rest twin from the moving twins perspective he is at rest and the at rest twin is the one moving. Therefore the moving twin observes the clock of the at rest twin going slower. The moving twin's clock is really the one going slower and the at rest twin will accurately observate that. THAT is the paradox. The paradox is resolved when the moving twin turns around and returns home. What you have claimed as paradox is just time dilution such that Tmoving twin = Trest twin * gamma

Video disclaimer: No math involved. 4 Doritos later… f 🟰✔️1+0.6 / 1 - 0.6 fo Morale: can’t explain relativity without math EVER!

Thanks for acknowledging that that KZbinrs haven’t done a good job of explaining the twin paradox, and always do so with some amount of hand waving. It’s the one piece about GR I’ve never felt like I’ve understood fully

Cool graphics. You'll do good

Fire video, hope this blows up