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I'm not sure who this is supposed to be useful to; I'm not sure how anybody can understand it unless they have completed an undergraduate degree in math AND alr

by powera 5y ago

I'm not sure who this is supposed to be useful to; I'm not sure how anybody can understand it unless they have completed an undergraduate degree in math AND already have a solid conceptual understanding of relativity. It is extremely dense.

pvg 5y ago
The same can be said for, say, Lifshitz & Landau's textbooks. A little bit closer to earth, Axler's Linear Algebra Done Right is well-liked and popular but of relatively little use to people trying to do linear algebra right for the fist time.
goldenkey 5y ago
I disagree. Most of relativity comes from the fact that all objects have an average velocity of their fundamental constituents. The highest average velocity is C, when the object is a beam of electromagnetic energy. This is why it takes infinite energy to accelerate an object to the speed of light, you can add more photons to it, but the average will always be less than C, you just get it slightly closer. The reason for time dilation and the other facets of relativity pretty much come down to the fact that objects either move or change, but cannot do both simultaneously. One can think of time passing inside a spacecraft or object as internal movement, as oppose to the external movement of the spacecraft throughout the cosmos. Each bit of energy provides h (Planck's constant) action, a measure of change of state. The more the object allocates toward external movement in space, the less it can allocate for internal movement / internal changes, which is what observer time really is. Even though I say external vs internal, I am not violating relativity. The reference frames are relative, we do not need an absolute reference frame. Doubly special relativity deduces most of these elegant derivations by assuming there is a smallest quanta of energy possible, but nonetheless, these concepts can be derived just by understanding the role of mass as loops of energy, energy as an allowance for change of state, and time as the usage of energy for internal change of state, and movement as the usage of energy for external change of state. Relativity is just the consequence of energy's connection to information and movement. https://en.wikipedia.org/wiki/Doubly_special_relativity https://en.wikipedia.org/wiki/Doubly_special_relativity
- AnimalMuppet 5y ago
  Um, no. That is not how any of that works. For instance, your second paragraph: No, objects move or change at the same time, just at different rates. And an object can be moving in one frame of reference, and only "changing" (time passing) in another.
  - goldenkey 5y ago
    I made my point clear, the amount of change of state that an object can produce over time, is given by its energy. This is because action equals joule-seconds, so energy equals actions per second. Just because you can change your frame to see change differently (ie. stationary) doesn't invalidate the point. This principle applies just as well even as the frame is changed. https://en.wikipedia.org/wiki/Action_(physics) https://en.wikipedia.org/wiki/Action_(physics)
- Koshkin 5y ago
  > average velocity of their fundamental constituents An interesting (if unusual) viewpoint; I wonder if this could lead to (a more realistic) quantum gravity. > objects either move or change, but cannot do both simultaneously This does make time slowing down inside a moving object kind of obvious. (I wonder if this description based on action/energy quantization turns out to be equivalent, at a certain level, to the essentially geometric picture of the classical relativity.)
  - goldenkey 5y ago
    It is indeed a very geometrical picture since position is just as much of a state as spin is. Position just has a few huge dimensions as its degrees of freedom. We don't know _yet_ whether position is continuously valued or discrete. Gravity being quantum would most likely indicate that position is also discrete. Since all energy, being allocated for external movement or just internal time, produces the same amount of gravity, it appears that the act of any state change induces gravity. Einstein never really gave a physically understandable reason for why all change causes gravitation, but it's likely similar to a ship in water. If the ship is rocking really fast, the waves that emanate from it can pull objects towards it. The rocking is just state change and even for a rest mass, we know that it's a loop of energy, there really is no static storage of mass.. it's a process of energy containment and cyclic change.
fferen 5y ago
Any particular suggestions? Although it is compact, I have tried to carefully choose the wording and arrange the sections so each concept builds on the last. Also, I intentionally avoid unnecessary mathematical abstraction; for example, the abstract definition of manifolds using coordinate charts, and tangent vectors as differential operators. This really tripped me up when trying to learn GR from standard textbooks.
- mhh__ 5y ago
  Needham's latest book might be a good source of intuition to "borrow" from for geometry.
- deleted 5y ago
  [deleted]
- powera 5y ago
  Maybe call it "The Mathematics of Relativity"? It works well as an outline from my point of view, but I think you have to assume the reader already understands the Lagrangian in classical physics (which is a stretch for even the comparatively well-educated Hacker News audience). Also, somewhere around 3.5 it gets too dense with material I don't already know. (Christoffel symbols? Riemann curvature tensor?) And then in the General Relativity section, there's simply too much material covered for any of it to be explained in depth beyond the necessary equations. I would drop the fluids (at a minimum) to give more space for other topics.
mhh__ 5y ago
That describes the usual general relativity student though.
BeetleB 5y ago
> I'm not sure how anybody can understand it unless they have completed an undergraduate degree in math AND already have a solid conceptual understanding of relativity. The prerequisites are clearly listed: > Prerequisites: vector calculus and classical mechanics Do you not find this accurate? (Note that classical mechanics means the typical physics undergrad classical mechanics - where you know diff eq and things like Lagrangians and calculus of variations).
dieselerator 5y ago
That seems a reasonable complaint. For relativity with more explanation and not much math I suggest Relativity (The Special and the General Theory) by Albert Einstein, 1916. Translated to English: ISBN 0-517-029618 I think the book is still in print, and new and used copies are cheap if you shop around. It is good reading if you want the details explained step by step.
jvvw 5y ago
For those of us with that background, it looks like it might be really useful though. I've only had a brief look so far, but as somebody who took all the pure courses in my maths degree, I've been looking for something a bit like this!

by powera 5y ago

pvg 5y ago

The same can be said for, say, Lifshitz & Landau's textbooks. A little bit closer to earth, Axler's Linear Algebra Done Right is well-liked and popular but of relatively little use to people trying to do linear algebra right for the fist time.

goldenkey 5y ago

I disagree. Most of relativity comes from the fact that all objects have an average velocity of their fundamental constituents. The highest average velocity is C, when the object is a beam of electromagnetic energy. This is why it takes infinite energy to accelerate an object to the speed of light, you can add more photons to it, but the average will always be less than C, you just get it slightly closer. The reason for time dilation and the other facets of relativity pretty much come down to the fact that objects either move or change, but cannot do both simultaneously. One can think of time passing inside a spacecraft or object as internal movement, as oppose to the external movement of the spacecraft throughout the cosmos. Each bit of energy provides h (Planck's constant) action, a measure of change of state. The more the object allocates toward external movement in space, the less it can allocate for internal movement / internal changes, which is what observer time really is. Even though I say external vs internal, I am not violating relativity. The reference frames are relative, we do not need an absolute reference frame. Doubly special relativity deduces most of these elegant derivations by assuming there is a smallest quanta of energy possible, but nonetheless, these concepts can be derived just by understanding the role of mass as loops of energy, energy as an allowance for change of state, and time as the usage of energy for internal change of state, and movement as the usage of energy for external change of state. Relativity is just the consequence of energy's connection to information and movement. https://en.wikipedia.org/wiki/Doubly_special_relativity https://en.wikipedia.org/wiki/Doubly_special_relativity

AnimalMuppet 5y ago
Um, no. That is not how any of that works. For instance, your second paragraph: No, objects move or change at the same time, just at different rates. And an object can be moving in one frame of reference, and only "changing" (time passing) in another.
- goldenkey 5y ago
  I made my point clear, the amount of change of state that an object can produce over time, is given by its energy. This is because action equals joule-seconds, so energy equals actions per second. Just because you can change your frame to see change differently (ie. stationary) doesn't invalidate the point. This principle applies just as well even as the frame is changed. https://en.wikipedia.org/wiki/Action_(physics) https://en.wikipedia.org/wiki/Action_(physics)
Koshkin 5y ago
> average velocity of their fundamental constituents An interesting (if unusual) viewpoint; I wonder if this could lead to (a more realistic) quantum gravity. > objects either move or change, but cannot do both simultaneously This does make time slowing down inside a moving object kind of obvious. (I wonder if this description based on action/energy quantization turns out to be equivalent, at a certain level, to the essentially geometric picture of the classical relativity.)
- goldenkey 5y ago
  It is indeed a very geometrical picture since position is just as much of a state as spin is. Position just has a few huge dimensions as its degrees of freedom. We don't know _yet_ whether position is continuously valued or discrete. Gravity being quantum would most likely indicate that position is also discrete. Since all energy, being allocated for external movement or just internal time, produces the same amount of gravity, it appears that the act of any state change induces gravity. Einstein never really gave a physically understandable reason for why all change causes gravitation, but it's likely similar to a ship in water. If the ship is rocking really fast, the waves that emanate from it can pull objects towards it. The rocking is just state change and even for a rest mass, we know that it's a loop of energy, there really is no static storage of mass.. it's a process of energy containment and cyclic change.

fferen 5y ago

Any particular suggestions? Although it is compact, I have tried to carefully choose the wording and arrange the sections so each concept builds on the last. Also, I intentionally avoid unnecessary mathematical abstraction; for example, the abstract definition of manifolds using coordinate charts, and tangent vectors as differential operators. This really tripped me up when trying to learn GR from standard textbooks.

mhh__ 5y ago
Needham's latest book might be a good source of intuition to "borrow" from for geometry.
deleted 5y ago
[deleted]
powera 5y ago
Maybe call it "The Mathematics of Relativity"? It works well as an outline from my point of view, but I think you have to assume the reader already understands the Lagrangian in classical physics (which is a stretch for even the comparatively well-educated Hacker News audience). Also, somewhere around 3.5 it gets too dense with material I don't already know. (Christoffel symbols? Riemann curvature tensor?) And then in the General Relativity section, there's simply too much material covered for any of it to be explained in depth beyond the necessary equations. I would drop the fluids (at a minimum) to give more space for other topics.

mhh__ 5y ago

That describes the usual general relativity student though.

BeetleB 5y ago

> I'm not sure how anybody can understand it unless they have completed an undergraduate degree in math AND already have a solid conceptual understanding of relativity. The prerequisites are clearly listed: > Prerequisites: vector calculus and classical mechanics Do you not find this accurate? (Note that classical mechanics means the typical physics undergrad classical mechanics - where you know diff eq and things like Lagrangians and calculus of variations).

dieselerator 5y ago

That seems a reasonable complaint. For relativity with more explanation and not much math I suggest Relativity (The Special and the General Theory) by Albert Einstein, 1916. Translated to English: ISBN 0-517-029618 I think the book is still in print, and new and used copies are cheap if you shop around. It is good reading if you want the details explained step by step.

jvvw 5y ago

For those of us with that background, it looks like it might be really useful though. I've only had a brief look so far, but as somebody who took all the pure courses in my maths degree, I've been looking for something a bit like this!