Ghideon

Why? I said the internals (beyond event horizon) of a black hole is not observable, and will not ever be observable as long as current models are considered. But the outside? See https://eventhorizontelescope.org. I do not see how your statement about black holes, dark matter, dark energy and "unobservable" matches what we currently know.

Please post details here and someone will have a look.

A black hole's interaction with its surroundings is observable. As is dark matter's interactions via gravitation. In the future dark matter may be directly detected. Internals of a black hole not so, according to current models. Internals of a black hole is unobservable even in principle.

Good points! I was only considering what, AFIK, is possible in our universe. Question about first one; would multiple objects, separated by enough space to be causally not connected, be the same situation mathematically? I mean, before the objects would have had a chance to affect each other, would the same math apply to each object? The object could be one of several in the universe but must be alone in its own observable region of the universe. (Example: gravitational waves propagating at light speed.) Note: I'm not stating that you comment is incorrect, just that I got curious about how this works in the context of the original question stated.

I think I get your point, I'll try to formulate a comment as part of my learning* about this: We have observations supporting models today that are limited; they do not reach all the way back to or beyond time=0. (But they get pretty close). Any model anyone may come up with, that extents beyond what we know today, must contain some changes and rate of change. A model with no measure of duration or rate of change will not make sense. It does not matter much what kind of model someone will present, what that is that is changing or how thins are changing. We still need a degree of freedom (dimension) for rate of change in any such model. Interpretations of models are also not really important at that point, important is that we can't do a model without a dimension describing rate of change or durations (AKA time). So: It never makes sense to ever create a model of the universe where time is not existing. Correct? *) Your skill in these matters are far greater than mine; I've better try.

Interesting, I’ll try to comment! Since our models fail to describe, and observations can not observe, the very earliest time, are we sure that time existed in the same sense as we define and observe it today? I mean, do we even know if ”beginning” makes sense?

True! I need to change use of words: Maybe this is better: If you start to exist at position (x,y,z) at time=t then you would be moving in reference to other observers. "Start to exist" in this case means that you, the matter you are created from, did not exist in the universe at time<t.

That sounds like a reactionless drive? Given that such things are impossible when current laws of physics (Newton, Lagrange, Hamilton etc) are correctly used we can safely assume that the Lagrange equations are incorrectly used in the analysis. If you have discovered new physics where current laws does not apply, please post references/evidence, that would be interesting to discuss!

Good description, better that the one I was writing. Note: I interpreted "Actually stationary" as stationary relative to some kind of absolute space since that was in the context of the old thread. My answer was/is slightly more complicated than necessary since the question referenced my post where an article where older and obsolete models of space-time were mentioned. Older/alternative models could give other answers, but that would not be compatible with current observations AFIK. Since the article you reference does not seem support object magically popping into existing I still think my line of thought regarding coordinates of position xyz is valid. Even if you could pop into existence (you can't) there is no location or time when such a popping into existence could take place and making you absolutely stationary. There is no absolute space at this time and I don't know of evidence that there ever was a time where space could have been absolute. Again, that does not necessary hold for older models in the article I referenced.

Can you point to a reference? See my last three points regarding Big bang and coordinates. You would, at least, have your frame of reference? How would momentum be defined in such a case where no frame of reference exists?

You would be stationary in your frame of reference. But not in other frames of reference; (x,y,z) is not an absolute point in space according to current models of spacetime. Does this answer your question? Some questions to use in case you want further discussion and details. -How did you get to position (x,y,z) without experiencing an accelerating force? Or how did the particles you are made of get to (x,y,z)? -If you (magically) popped into existence at position (x,y,z) then you would be moving in reference to other observers, how about conservation of momentum? -If you avoid the points above somehow; what about expansion of the universe? In what coordinate system is your position a stationary position?

Thanks! Short answer: select the course. Longer answer: I agree with the good answer provided by @timo . The list is rather basic and very useful as a basis for may other areas. I would like to add some notes. Do a strategic analyse: Are you interested in math? Are you interested in science? What areas are you going to work in? Will there be competition for interesting positions within your areas of interest? Will better math skill give you advantage comparing to other individuals? Will you be interested in moving towards other areas where more math is needed Will you stay in the business when current technology and concepts are replaced by new ones? Are there many other optional sources that are more important to you? Will you have to skip something? Personal opinions: Math skills makes it easier to communicate with stakeholders in various engineering areas and understanding their domains, projects and issues. One never know which type of new math skills is required for a position or during an assignment so grasping the basics is a good start, makes it easier to move on to more advanced things later. In daily work with AI or Machine learning using common APIs of today there is not much use for calculus during coding or system design. But other areas of math, that I personally studied after the calculus topics in your list, is more useful on daily basis. (For instance statistics and numerical methods) Had this question been asked while I was at the university I would maybe have told you to skip the course. I did calculus and some more math when studying computer science and engineering.

I did a test to verify my idea above: Search history in google while logged in on google account (used for gmail etc), plenty of entries: c Log out from google account (gmail) and clear browser history. There are no entries in search history: Log in on google again, then there are entires again even if browser history was cleared (I have hidden the text due to privacy since the order of entries was not the same): So I insist, check what online services that are in use and if any of them keeps history (like google above) so that it is not enough to clear the browser history. In the case of google, check the history and history settings on myactivity.google.com/myactivity.

Hello. I have some experience from this. Can you provide some examples what's included in calculus in your case? My studies was likely in another country and university so I would like some more context, then I'll try to answer.

Obvious answer is as @Curious layman says, but are you logged in somewhere? Does the history come from brower or from somewhere else, such as a google account?

Thanks, good to know that the description was helpful! This, and related topics have been discussed by many through the ages. In case you are interested here is a reference with various ideas held by Descartes, Newton, Leibniz and others, https://plato.stanford.edu/entries/spacetime-theories/: "Since antiquity, natural philosophers have struggled to comprehend the nature of three tightly interconnected concepts: space, time, and motion. A proper understanding of motion, in particular, has been seen to be crucial for deciding questions about the natures of space and time, and their interconnections. Since the time of Newton and Leibniz, philosophers' struggles to comprehend these concepts have often appeared to take the form of a dispute between absolute conceptions of space, time and motion, and relational conceptions. This article guides the reader through some of the history of these philosophical struggles."

How do you define a point in space? 1: If you try to define a point in space as XYZ and have no other object to compare against, how do you know if you are stationary or moving at a constant* speed relative to the point you just defined? 2: If you try to define a point in space as XYZ and have one other object to compare against, how do you know if you are moving or if the other object is moving or both are moving at a constant speed? You can define a point XYZ in your frame of reference, or someone else's frame of reference, but not a point XYS in space. Space (spacetime) is not absolute. If you see any object moving in space from x1y1z1 to x2y2z2 it is between two points relative to you, not between two points in space. *) Note that I say constant speed. Acceleration can be measured.

I reread the above, it is a good example covering several aspects of the consequences of how light behaves the same, in addition to propagating at an invariant speed. -Light, and processes that depends on speed of light, is same everywhere, distant stars behave the same. -How light is affected by propagating from distant stars to earth is understood and modelled. -How light interact with matter on earth is understood. One result is Astronomical spectroscopy*; lots of properties of distant stars (and other objects) can be studied since the behaviour of light is the same. *) https://en.wikipedia.org/wiki/Astronomical_spectroscopy (not limited to visible light that this topic is about)

I must be able to actually see answers to my questions, otherwise the answers does not exist.

Neat! Just as a photo; the oldest photo of a person shows the events when that person was youngest.

If space is reversed, what do you mean by centre, inside, outside, approach, outer space? It is tricky to visualise from which point of view you are using these terms and if they mean the opposite or not. When saying "looks like" does that mean that light is traveling from a source to and observer or that it is some mathematical concept? Or something other? If space is reversed so the event horizon is the center isn't then all the mass distributed on the event horizon? If the mass is still in the center and "Relativity obeys the same rules out here as it does in there" then there is no reversal of space?

Why not spend more time preparing for explaining the theory?

Does the big bang have a range? What is that?

Another thought, if you drop the name "dimension" and "realm" and add math supported by confirmed observations, how far would you be from the already accepted concept "Quantum superposition"? Are your imprecise statements trying to describe something already known?

Personal opinion, other members may disagree: If you haven't done so already, start by taking a look at Special Relativity. The math is not very advanced and it is possible to understand lots of the details in the mathematical model with limited effort. At least compared to General relativity or Quantum theories for instance. But once you grasp how for instance Lorentz transformations are calculated the math starts telling you consequences of Einsteins postulates. You will look at formulas and see for instance how they will approximate Newton at low speeds or how it is obvious that observers in different frames of reference will disagree about time. Time dilation is no longer some concept heard in a popsci tv program, it will be something you see emerge from the experimentally confirmed model.