1. Are gravitational forces and mass relative to structure and size? i.e. Earth/Mars. Thanks, Peace!

2. ### Related Discussions:

3. Can you explain your question in a little more detail ? It is not really clear what you mean by this. Thanks.

4. The force of gravity is determined by Newton's formula (for simple cases, like this):

Where M is the mass of the planet, m is the mass of an object, and r is the radius of the planet. The force is pretty much what we perceive as weight.

So the more massive the planet, the greater the gravity. The larger the radius, the smaller the (surface) gravity.

5. if i have a hollow sphere, like a malteser, but it is more dense on one side, will i experience a stronger grav pull on that side?

6. Yes, because you will be closer to the centre of mass of the sphere.

7. Originally Posted by Strange
The force of gravity is determined by Newton's formula (for simple cases, like this):

Where M is the mass of the planet, m is the mass of an object, and r is the radius of the planet. The force is pretty much what we perceive as weight.

So the more massive the planet, the greater the gravity. The larger the radius, the smaller the (surface) gravity.
Strange, I am having trouble getting my head around your statement " The larger the radius, the smaller the (surface) gravity "

8. Originally Posted by Dave Wilson
Originally Posted by Strange
The force of gravity is determined by Newton's formula (for simple cases, like this):

Where M is the mass of the planet, m is the mass of an object, and r is the radius of the planet. The force is pretty much what we perceive as weight.

So the more massive the planet, the greater the gravity. The larger the radius, the smaller the (surface) gravity.
Strange, I am having trouble getting my head around your statement " The larger the radius, the smaller the (surface) gravity "
He means assuming the same mass. But it does have counter-effect in general practice also. Consider the Earth and Moon, the Earth is 81 time more massive than the Moon, but because its surface is ~3.67 times further from its center, the surface gravity is only ~6 times greater than that of the Moon's.

9. OK Dude.

10. Thanks Janus. That was exactly what I meant to say...

11. Thanks for the input!
In the same or similar way is gravitational force applied to mass in situations where sub atomic particle are the example...If that makes sense?

12. Originally Posted by ampwitch
Thanks for the input!
In the same or similar way is gravitational force applied to mass in situations where sub atomic particle are the example...If that makes sense?
Do you mean, are subatomic particles affected by gravity? If so, then yes. After all matter is just a collection of subatomic particles. That is what contributes to the vast majority of the mass of a body (a tiny amount comes from the energy holding the particles together).

13. Two thoughts:1. Without coming across as funny is it the case that without mass there is no gravity?
2. Is the mass of energy as in E=MC-squared always the end product or the same as? In other word is energy the result of mass & C-squared such that one is necessary for the other...? Thanks!

14. Originally Posted by ampwitch
Two thoughts:1. Without coming across as funny is it the case that without mass there is no gravity?
No, it isn't. Energy (and various other things, including gravity itself) create/contribute to gravity.

2. Is the mass of energy as in E=MC-squared always the end product or the same as? In other word is energy the result of mass & C-squared such that one is necessary for the other...?
I'm not quite sure about your wording, but the equation simply says how much energy you would get if you converted a given amount of mass into energy (or mass into energy). That amount of mass has the same gravitational effect as the equivalent amount of energy.

15. Originally Posted by ampwitch
1. Without coming across as funny is it the case that without mass there is no gravity?
No, like Strange said, energy causes gravity. You can see references to this in Einstein's original work, where he says stuff like "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy".

Originally Posted by mpwitch
2. Is the mass of energy as in E=MC-squared always the end product or the same as? In other word is energy the result of mass & C-squared such that one is necessary for the other...?
It's the other way round. The mass of a body is a measure of its energy-content, see Einstein's E=mc² paper. He uses L instead of m, and he talks about a radiating body losing mass. In similar vein you could trap massless radiation in a mirror-box, whereafter it's harder to move the box.

16. Thanks a lot for the input. I read the link article...very helpful. Sorry about wording.

17. Originally Posted by Farsight
Originally Posted by mpwitch
2. Is the mass of energy as in E=MC-squared always the end product or the same as? In other word is energy the result of mass & C-squared such that one is necessary for the other...?
It's the other way round. The mass of a body is a measure of its energy-content
Huh? Mass and energy are entirely equivalent under this theory; it;s a two-way street

In fact physicists routinely work in units where . This allows them to refer to the mass of a a sub-atomic particle in terms of electron-volts

You can see references to this in Einstein's original work, where he says stuff like "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy"
And what exactly do YOU think he means by "the energy of a gravitational field"?

18. Most physicist are making the mistake of applying a gravity constant measured between two metal balls on earth, then removing it from it's inertial frame of reference and then using it to reverse engineer the mass of other planetary objects, be very careful with that.

19. Originally Posted by ttown
Most physicist are making the mistake of applying a gravity constant measured between two metal balls on earth, then removing it from it's inertial frame of reference and then using it to reverse engineer the mass of other planetary objects, be very careful with that.
Do you have some evidence that Newtonian gravity or General Relativity is wrong?

20. Originally Posted by Strange
Originally Posted by ttown
Most physicist are making the mistake of applying a gravity constant measured between two metal balls on earth, then removing it from it's inertial frame of reference and then using it to reverse engineer the mass of other planetary objects, be very careful with that.
Do you have some evidence that Newtonian gravity or General Relativity is wrong?
Yes, Newton himself said that you can not apply it outside its' inertial frame of reference.

21. Originally Posted by ttown
Yes, Newton himself said that you can not apply it outside its' inertial frame of reference.
I didn't know that. Can you provide a reference for where he said that and what he meant?

But, as you know, any shortcomings with Newtonian gravity are solved by GR. No?

22. Originally Posted by Strange
Originally Posted by ttown
Yes, Newton himself said that you can not apply it outside its' inertial frame of reference.
I didn't know that. Can you provide a reference for where he said that and what he meant?

But, as you know, any shortcomings with Newtonian gravity are solved by GR. No?
Fixed stars - Wikipedia, the free encyclopedia
Newton assumed and used "fixed stars" as an inertial frame of reference. The point i try to make is that the mass of planets has been derived from a constant established on earth between attraction between two steel balls, inertial frame of reference surface of earth. The is far and away from being an inertial frame of reference relative to background stars, (which even then not include other forces such as centrifugal force). So be careful with claiming mass of planets based only on their orbital distance and period.

23. Originally Posted by ttown
Fixed stars - Wikipedia, the free encyclopedia
Newton assumed and used "fixed stars" as an inertial frame of reference. The point i try to make is that the mass of planets has been derived from a constant established on earth between attraction between two steel balls, inertial frame of reference surface of earth. The is far and away from being an inertial frame of reference relative to background stars, (which even then not include other forces such as centrifugal force). So be careful with claiming mass of planets based only on their orbital distance and period.
Do you have any evidence that the gravitational constant is different in different frames of reference?

24. Originally Posted by Strange
Originally Posted by ttown
Fixed stars - Wikipedia, the free encyclopedia
Newton assumed and used "fixed stars" as an inertial frame of reference. The point i try to make is that the mass of planets has been derived from a constant established on earth between attraction between two steel balls, inertial frame of reference surface of earth. The is far and away from being an inertial frame of reference relative to background stars, (which even then not include other forces such as centrifugal force). So be careful with claiming mass of planets based only on their orbital distance and period.
Do you have any evidence that the gravitational constant is different in different frames of reference?
It has never been measured.

25. Originally Posted by ttown
It has never been measured.
So you have absolutely no reason to think it is different?

26. Originally Posted by Strange
Originally Posted by ttown
It has never been measured.
So you have absolutely no reason to think it is different?
Big G and little g should not be confused. Big G is what it is, but using it to claim the mass of planetary objects based on orbital distance and period after removing G from its inertial frame of reference should be understood as such.

27. Originally Posted by ttown
Big G and little g should not be confused. Big G is what it is, but using it to claim the mass of planetary objects based on orbital distance and period after removing G from its inertial frame of reference should be understood as such.
But you still haven't said what reason you have for thinking that G is different in different frames of reference. Or what we should use instead. It is easy to say, "all physics might be wrong" especially when you have no evidence and no alternative.

28. Originally Posted by ttown
It has never been measured.
That wasn't the question. And we don't still use steel balls to measure it, either.

The question was: Do you have any evidence the gravitational constant is not constant across different frames of reference? Any observations of stars or planets or galaxies acting differently to our own? Any evidence that the physical constants are not constant across the universe? Any reason to think the gravitational constant is different in other places?

29. Originally Posted by ttown
Big G and little g should not be confused. Big G is what it is, but using it to claim the mass of planetary objects based on orbital distance and period after removing G from its inertial frame of reference should be understood as such.
Why do you keep referring to Newton and inertial frames of reference? We use General Relativity nowadays, and in GR the notion of inertial frames of reference was changed somewhat.

I mean, Newtonian gravity doesn't even accurately describe the orbit of Mercury, whereas General Relativity does.

30. There are several other forces at work, and ignoring them and using G by itself can not explain a lot of the structure that we can see in the universe. You will probably need something to explain some force that acts on the difference between the forces of two mass objects. Coulomb was able to understand this pretty well.

31. Originally Posted by SpeedFreek
Originally Posted by ttown
Big G and little g should not be confused. Big G is what it is, but using it to claim the mass of planetary objects based on orbital distance and period after removing G from its inertial frame of reference should be understood as such.
Why do you keep referring to Newton and inertial frames of reference? We use General Relativity nowadays, and in GR the notion of inertial frames of reference was changed somewhat.
That's why we should not be using G by itself.

32. Originally Posted by ttown
There are several other forces at work, and ignoring them and using G by itself can not explain a lot of the structure that we can see in the universe. You will probably need something to explain some force that acts on the difference between the forces of two mass objects. Coulomb was able to understand this pretty well.
You were talking about using planetary orbits to determine mass. General Relativity describes the planetary orbits in the Solar System incredibly well already, which is why we use it. There are indeed many different factors that combine to cause the curvature of space-time, but I know we aren't talking about the same thing here, are we?

Is this a prelude to an exposition on plasma cosmology?

33. Originally Posted by Guitarist
Originally Posted by Farsight
...The mass of a body is a measure of its energy-content
Huh?
Huh yourself. That's a direct quote from Einstein's E=mc² paper. You might care to read it sometime. Alternatively start a thread and ask the question, and I'll be happy to explain it to you.

34. I am not sure how to write what I am thinking.
1. I suspected that the relationship between G and E were perhaps inseparable. I really appreciate all the input. Thanks, especially to speedfreak for correctly re-stating my question. Also the idea of G versus g is odd to think about but cool b/c it led to a question that I hope to thread at some near interval in time...Plasma U. but I don't know if it is a sour subject.?
2. Also I am trying to reckon with space-time curvature as a result of gravity...I think? Thanks! Peace
As a side note I am grateful that I was able to read bits of Newton's Cannonball explanation and also Einstein...amazing, and incredible stuff!!!

Thanks!

35. Originally Posted by Amanbir
I have done this, again, and again. I feel I am wasting my time.
Indeed you are.

Space and Time have nothing to do with one another.
If you say so

In fact, I went so far as to say that the Holocaust may have something to do with Einstein's work.
I think this is unacceptable. I should like to hear what the moderators think about this.

36. Amanbir,

I am giving you a day off. Once again, you are not allowed to post in the main sections, because it is only for accepted science, not your personal ideas about them. People are asking honest questions and you are providing them with nonsense. This is you last warning. Next time you suspension will be permanent.

37. Originally Posted by ampwitch
I am not sure how to write what I am thinking.
1. I suspected that the relationship between G and E were perhaps inseparable. I really appreciate all the input. Thanks, especially to speedfreak for correctly re-stating my question. Also the idea of G versus g is odd to think about but cool b/c it led to a question that I hope to thread at some near interval in time...Plasma U. but I don't know if it is a sour subject.?
2. Also I am trying to reckon with space-time curvature as a result of gravity...I think? Thanks! Peace
As a side note I am grateful that I was able to read bits of Newton's Cannonball explanation and also Einstein...amazing, and incredible stuff!!!

Thanks!
Well if you do an experiment and create plasma along the outside of the wire, it is quite interesting, the plasma will flow in both directions in a double helix with the currents flowing in both directions back to its' respective poles. Then you look out into space and see various space matter and gases organizing themselves into this same double helix structure. I wonder what could be flowing in opposite directions to cause this matter to twist around itself in this fashion?

38. Originally Posted by SpeedFreek
Is this a prelude to an exposition on plasma cosmology?
That would be an affirmative, then.

39. Originally Posted by Farsight
Originally Posted by Guitarist
Originally Posted by Farsight
...The mass of a body is a measure of its energy-content
Huh?
Huh yourself. That's a direct quote from Einstein's E=mc² paper.
As you are apparently still bothered by this: I thought it was pretty obvious that the "Huh?" was a reference to the part of the post you omitted: "It's the other way round."

It's not "the other way round". Or, at least, as Guitarist said (which you also chose to leave out for some reason) it is both ways round.

40. I'm not bothered, Strange. Guitarist said Huh? Mass and energy are entirely equivalent under this theory; it;s a two-way street. It isn't. Photon energy and momentum are given as E=hf and p=hf/c, but rest mass does not apply to a photon.

41. Who are you people

Is the CIA working this? You have to tell me, I'll find some place else to be.

42. Originally Posted by Farsight
I'm not bothered, Strange. Guitarist said Huh? Mass and energy are entirely equivalent under this theory; it;s a two-way street. It isn't. Photon energy and momentum are given as E=hf and p=hf/c, but rest mass does not apply to a photon.
Just use the relativistic energy-mass-momentum relation :

For massless particles like the photon you get E=pc, for particles at rest you get E=mc^2, as expected. I don't really see the issue here.

43. Originally Posted by Amanbir
Who are you people

Is the CIA working this? You have to tell me, I'll find some place else to be.
Not the CIA; it's just a world-wide conspiracy to protect scientific-religious dogma from progressive-thinking people with superior intellects

44. Yep, that's it.

But guess what, I'm still here..

And don't run from me , fight me, if you have that you speak of.

45. Originally Posted by Amanbir
And don't run from me , fight me
Not interested, because it's pointless. Just having ourselves a little fun before the inevitable end

46. "Is this a prelude to an exposition on plasma cosmology" No, but since you asked about Plasma U. and since I have an interest in the idea/theory I thought I would try to get an idea about it's general acceptance. Mostly the M,G question rose on account of the Higgs Discovery. In that I was more interested in the rate of decay and the effect gravity has in relation to it's/that decay if that makes sense. Unfortunately I am not clear enough on it to present the question in any more formal way. Thanks! Peace!!

47. Originally Posted by Farsight
rest mass does not apply to a photon.
As compared to what other sort of mass?

48. Originally Posted by Markus Hanke
Originally Posted by Amanbir
Who are you people

Is the CIA working this? You have to tell me, I'll find some place else to be.
Not the CIA; it's just a world-wide conspiracy to protect scientific-religious dogma from progressive-thinking people with superior intellects
In other words, the grand order of SADO (Self-Appointed Defenders of the Orthodoxy).

49. Originally Posted by Janus
Originally Posted by Markus Hanke
Originally Posted by Amanbir
Who are you people

Is the CIA working this? You have to tell me, I'll find some place else to be.
Not the CIA; it's just a world-wide conspiracy to protect scientific-religious dogma from progressive-thinking people with superior intellects
In other words, the grand order of SADO (Self-Appointed Defenders of the Orthodoxy).
Yes, the SADOs and their pseudoscience. Maybe they should do more experimentation before pushing their papers theories based on someone else's logically flawed idea that they never observed themselves.

50. Originally Posted by Guitarist
As compared to what other sort of mass?
There's relativistic mass which is a measure of energy. Then there's passive gravitational mass which is a measure of the response to a gravitational field. Essentially the same thing is active gravitational mass, which is again a measure of energy because it's a concentration of energy that results in a gravitational field. There's also inertial mass which is the same as active gravitational mass. The photon doesn't have inertial mass in the sense that you can slow it down. However it conveys inertia, and you can "decelerate" it in the vector sense via Compton scattering. It offers resistance to a change in its state of motion, and in that sense it does have inertial mass.

Whilst all these terms feature the word "mass", common parlance in physics is that unless qualified, mass means rest mass. This does not apply to the photon because it's always measured to be travelling at c and isn't at rest. There's also invariant mass which is usually thought of as being the same as rest mass. For your amusement and delectation: invariant mass is a misnomer, because it varies in a gravitational field.

51. invariant mass is a misnomer, because it varies in a gravitational field.
Weight varies in a gravitational field, not mass.

52. I meant what I said. Invariant mass varies. See Mass in general relativity. See where it says "Surprisingly, the answer is no".

Throw a cannonball up into the air, watch it rise up a metre, then just before it starts to fall back down again, think fast...

You did work on that cannonball. You expended energy. You gave the cannonball some kinetic energy, and that kinetic energy has now become gravitational potential energy. But where is this gravitational potential energy? No, it isn't in the gravitational field. Even a kid could work that one out. Because with a little help from your friends at NASA, you could throw that cannonball up into the air at 11km/s. It's then lost from the system, forever trundling through space, and the Earth's gravitational field is now reduced a little. The Earth's gravitational field didn't acquire all your kinetic energy. So where can it have gone? Yes, it's in the cannonball.

Yes, the cannonball poised a metre in the air comprises more energy the same cannonball sitting on the ground. Its "invariant" mass is greater than it was. As it falls to the ground, gravity doesn't do work on it, it just liberates some of the cannonball energy as kinetic energy. If we say this is radiated away into space and lost to the system, the total system energy is now reduced. This reduction is known as binding energy, and by convention is considered to be negative. It isn't really negative energy, it's just less positive energy. The cannonball has lost this energy, and by virtue of mass-equivalence, its invariant mass is reduced to its former value. It lost mass just as surely as a red-hot cannonball on the ground is a radiating body that loses mass, just like Einstein said.

53. Originally Posted by Farsight
For your amusement and delectation: invariant mass is a misnomer, because it varies in a gravitational field.
"Invariant" is not the same as "constant" - it means it remains unchanged under some transformation. In the context of SR an "invariant" quantity is one that is the same for all inertial observers ( i.e. invariant under Lorentz transformations ), but that doesn't mean it is constant.

Invariant mass varies.
See above. It can vary, but it varies the same way for all inertial observers.

54. Noted Markus. You'll maybe be aware from previous conversations that I don't concur with the sentiment "if Lorentz invariance is seen to fail, relativity fails too". Instead I see this as a minor conflict with the principle of equivalence requiring a slight qualification. One for another day perhaps.

55. [/QUOTE] Do you have any evidence that the gravitational constant is different in different frames of reference? [/QUOTE]

Not frame of reference, but another energy system, think along systems with boundaries.

It is just a thought, albeit a brilliant one.

56. In relation to gravity: is or does gravity have an internal tension? I would like to read more on that question. Thanks! Peace!

57. Originally Posted by ampwitch
In relation to gravity: is or does gravity have an internal tension? I would like to read more on that question. Thanks! Peace!
I'd say no and yes. If you look at the stress energy tensor article on wikipedia, you can see mention of shear stress, and pressure. Stress is "directional pressure" and like pressure, is measured in Pascals. Tension doesn't feature, a tensor is merely a matrix, so initially I'd say no, gravity does not have an internal tension

The caveat yes goes like this: remember that stress is negative tension, and think of a bow and arrow. Nock the arrow, then draw the bow, and hold it there. There's stress along your arm and around the curve of the bow, and there's tension in the drawstring. The arrow isn't going anywhere because the stress and tension are in balance. In similar vein a gravitational field "isn't going anywhere", so the stress must be balanced by a tension. The nature of this relates to the strong force and unification, and is physics beyond the standard model.

58. Originally Posted by ampwitch
Are gravitational forces and mass relative to structure and size? i.e. Earth/Mars. Thanks, Peace!
Yes, take Halleys Comet and other irregular comets and asteroids for instance. The positioning of the mass given its structure and sizes cause the object to orbit, itself. Also at different parts of the Earth where the density of mass is greater the gravitational pull is also stronger. I believe this has something to do with the allignment of mass.

This effect is present in the Sol System Barycentre in which the Sun will rotate further away from its average centre of mass by a greater degree when the planets are in allignment with one another, the greater the mass in line with the centre of gravity the stronger the force of gravity.

59. I don't understand "matrix" in gravitation...? Peace!

60. A matrix is just a mathematical way of expressing things, see http://en.wikipedia.org/wiki/Matrix_(mathematics) and say Tensors, Stress, Strain, Elasticity to get the gist of it.

61. Originally Posted by Farsight
I'm not bothered, Strange. Guitarist said Huh? Mass and energy are entirely equivalent under this theory; it;s a two-way street. It isn't. Photon energy and momentum are given as E=hf and p=hf/c, but rest mass does not apply to a photon.
Farsight is a great example of how someone can be entirely ignorant of physics yet claim the voice of authority on these matters because of some half-understood, cherry-picked references.

62. Originally Posted by Farsight
A matrix is just a mathematical way of expressing things
Which, on your part, is a vacuous way of expressing nothing meaningful at all.

Do you know what is a linear transformation on a vector space? Do you know that this transformation and the vector it operates on can be represented as matrices?

Do you know that the set of all invertible linear transformations on a vector space form a group, which is called - the general linear group - where is an n-dimensional vector space.

Do you know this group is a matrix Lie group, and has several very interesting subgroups - interesting both to mathematicians and to physicists.

I doubt that you do. Don;t spend too long Googling, you won't understand what you read......

63. Yes a matrix I understand, however being able to use a matrix to give some indication is difficult to understand. I think the problem is in setting up the matrix. In other words, if I assume a three dimensional object ( which may not be correct) and place the value assignment of the object to the matrix: what I am not certain of is how to make sense of the results no matter how basic the result might be. So if in one I find a value for G and then place a value for E and so forth I am not sure how to understand the result in a useful/meaningful way. I hope that makes sense. Peace!

64. Originally Posted by Guitarist
Do you know that the set of all invertible linear transformations on a vector space form a group, which is called - the general linear group - where is an n-dimensional vector space.
I wasn't aware of that - learned something new again

65. Originally Posted by Farsight
A matrix is just a mathematical way of expressing things, see http://en.wikipedia.org/wiki/Matrix_(mathematics) and say Tensors, Stress, Strain, Elasticity to get the gist of it.
Careful here - strictly speaking only rank-2 tensors can be represented by matrices, whereas the reverse is not true : not all matrices are rank-2 tensors. A tensor is a multilinear map which obeys a certain transformation law, making it independent of the coordinate basis, or else it isn't a tensor.
Just thought I'd point this out. I ran afoul of this important difference a number of times when I first started to learn about tensors.

66. Fair enough Markus.

Originally Posted by Guitarist
Which, on your part, is a vacuous way of expressing nothing meaningful at all...
It's meaningful enough, Guitarist.

Originally Posted by Guitarist
Do you know what is a linear transformation on a vector space? Do you know that this transformation and the vector it operates on can be represented as matrices?

Do you know that the set of all invertible linear transformations on a vector space form a group, which is called - the general linear group - where is an n-dimensional vector space.

Do you know this group is a matrix Lie group, and has several very interesting subgroups - interesting both to mathematicians and to physicists.
Sure I do. Now please, do try to contribute usefully to the discussion. As I've said previously, if I say something wrong or misleading please feel free to explain why. It isn't always easy to explain things simply, and I value feedback that will correct and improve such explanations. Alternatively you could offer a better explanation of your own, no problem with that.

It might be useful if you re-read the thread and took note that you haven't been doing either, and instead you've been chipping in with spoiler quips and permitting the same from PhysBang. I have to say that we expect something rather better than that from a moderator.

67. Originally Posted by Farsight
Sure I do {know about linear transformations, the General Linear Group and Lie groups in general}.
Very good. Then please argue why the notation I gave is not the most general one, and why one uses instead the notation for real valued vector spaces and for complex valued ones.

Now prove that these are indeed groups and that therefore their subsets are too.

Now prove that these are also manifolds and their subgroups are too

For bonus points, explain the difference between the General Linear Groups and the Special Linear groups and their subgroups respectively

Then and only then will your assertion be believed.

And no, this is not a "quip", it is a serious question

68. Originally Posted by Guitarist
Very good. Then please argue why the notation I gave is not the most general one, and why one uses instead the notation for real valued vector spaces and for complex valued ones.

Now prove that these are indeed groups and that therefore their subsets are too.

Now prove that these are also manifolds and their subgroups are too

For bonus points, explain the difference between the General Linear Groups and the Special Linear groups and their subgroups respectively

Then and only then will your assertion be believed.

And no, this is not a "quip", it is a serious question
Interesting. As a non-mathematician I may try my hand at this, but only after Farsight has given his answer.

69. Originally Posted by Guitarist
Very good. Then please argue why the notation I gave is not the most general one, and why one uses instead the notation for real valued vector spaces and for complex valued ones.
The expression you gave was:

It's a shorthand way of saying "the General linear group over an n-dimensional vector space". However a general linear group is a group of invertible linear transformations. In essence you can perform a transformation and then do its opposite to end up back where you started. However you can't necessarily do this with any old vector space. The expression is too generalised, and does not allow for non-commutability wherein the end result depends upon the sequence of transformations. The word for this is abelian. Instead the more pointed expression

is used for a real-valued vector space where n denotes the number of rows and columns of a "invertible" matrix representing that vector space, and the declares that vector space to be Euclidean. The expression

is given separately because a complex-valued matrix has two terms in each cell, and "has an extra dimension" to it. The distinction is important because in physics, complex numbers are associated with rotations, which do not necessarily commute.

Originally Posted by Guitarist
Now prove that these are indeed groups and that therefore their subsets are too.
No. Now that's enough Guitarist. Stop wasting my time. We both know that you'll either play the you copied it card, or alternatively you'll play the Emperor's New Clothes card and launch off into some irrelevant off-topic mathsdump spiel that most other posters do not understand. In either case those other posters are still sharp enough to see that you're driven by emotion: you fear that my physics knowledge surpasses yours. Why fear it? I don't fear the fact that your mathematics knowledge surpasses mine. Don't fear it. Get used to it.

Now, this thread concerns gravity and mass. Can we get back on topic please?

70. Ha, ha. First I note that in his attempt to explain why the notation is preferred over , Farsight assumes the truth of the point he is trying argue. This is considered poor hygiene in mathematics and, I should hope, also in physics

I further note he ducks out of any form of proof of the other questions I asked. Quel surprise

Originally Posted by Farsight
you're driven by emotion: you fear that my physics knowledge surpasses yours.
You are correct, the emotion I am driven by is anger that you set yourself up as a "physics guru" when anyone with even as little detailed knowledge of physics as me can see you are spouting BS. So no, I do not accept that your knowledge exceeds mine in any of the so-called hard sciences

Why fear it?
Actually I don't, principally because, although I freely confess my detailed knowledge of physics is limited, I remain unconvinced that yours is better - or even as great - as mine. At least I understand the language that physicists use, and you patently do not

71. I'm not spouting BS Guitarist, I'm talking about things you don't know about. My physics knowledge far surpasses yours. Get used to it and move on. Console yourself with the fact that your mathematics knowledge far surpasses mine.

Now, can we talk about gravity and mass please?

72. Originally Posted by Farsight
I'm not spouting BS Guitarist, I'm talking about things you don't know about. My physics knowledge far surpasses yours.
Well then, perhaps you would like to try your hand at the exercises I published on this thread :

Exercises in Physics

with many more to come. As you have probably read I have started all over again to study the basics to plug the holes in my own knowledge, and these exercises are from the classical mechanics section of my textbook. If your physics knowledge far surpasses Guitarist's, then those exercises should be no problem for you, should they ?

73. Originally Posted by Markus Hanke
Originally Posted by Farsight
I'm not spouting BS Guitarist, I'm talking about things you don't know about. My physics knowledge far surpasses yours.
Well then, perhaps you would like to try your hand at the exercises I published on this thread :

Exercises in Physics

with many more to come. As you have probably read I have started all over again to study the basics to plug the holes in my own knowledge, and these exercises are from the classical mechanics section of my textbook. If your physics knowledge far surpasses Guitarist's, then those exercises should be no problem for you, should they ?
His knowledge far surpasses that of everyone else's in a non-Euclidean sense. He's so far ahead that he's behind.

74. Thanks...this thread has helped me a lot, really! Again, Thanks! I am going to try the problem posted Exercises in Physics but will likely be far afield in my attempt.

75. Originally Posted by Guitarist
Very good. Then please argue why the notation I gave is not the most general one, and why one uses instead the notation for real valued vector spaces and for complex valued ones.
The first group would be one containing n x n invertible matrices with real-valued elements, the second one the same with complex-valued elements.
I don't know the answer to the first part though, because I would have thought that the notation in terms of a vector space is the more general one - perhaps you can explain this ? Does it have to do with the fact that vector spaces are dependent on a coordinate basis ?

Now prove that these are indeed groups and that therefore their subsets are too.
The elements of both groups fulfil the group axioms, because the following holds for the operation of matrix multiplication :

1. Closure : matrix multiplication of two n x n invertible matrices yields an n x n invertible matrix
2. Associativity : For matrix multiplication you have (a x b) x c = a x ( b x c )
3. Identity : There is an identity element under which a x e = e x a
4. Inverse Element : These are invertible matrices, so that a x b = b x a = e

Since the elements of the subgroups are elements of the main group, the axioms are trivially fulfilled for the subgroups as well.

Now prove that these are also manifolds and their subgroups are too
As per your own thread from a while ago one would need to prove that the local neighbourhood of every given point is homeomorphic to Euclidean space ( n-ball, I think you called it ). What I don't quite understand in this case is how to associate matrices ( which are the group elements here ) with points in a topological space. I don't really get the connection, maybe a short explanation would be in order.

For bonus points, explain the difference between the General Linear Groups and the Special Linear groups and their subgroups respectively
GL is the group of n x n invertible matrices. SL is the group of n x n invertible matrices with determinant = 1.

76. Originally Posted by Markus Hanke
Well then, perhaps you would like to try your hand at the exercises I published on this thread :

Exercises in Physics

with many more to come. As you have probably read I have started all over again to study the basics to plug the holes in my own knowledge...
With respect Markus, mathematical exercises will not plug the holes in your physics knowledge. If you prefer to tackle them using mathematics, I would advise you to study the terms in mathematical expressions and attempt to relate abstraction to reality. I had hoped you were beginning to do this when we were speaking about the short form of the Einstein field equations:

Ricci curvature tensor.
scalar curvature.
metric tensor.
cosmological constant.
Newton's gravitational constant.
speed of light in vacuum.
stress–energy tensor.

Originally Posted by Markus Hanke
...these exercises are from the classical mechanics section of my textbook. If your physics knowledge far surpasses Guitarist's, then those exercises should be no problem for you, should they?
I could do them eventually whilst Guitarist could just rattle them off. But what's the point? Writing down mathematical expressions for balls and planes and cones does not increase anybody's understanding of the basics. The basics are the terms, like those above, like E and p and m and c and C and h and t. To plug the holes in your physics knowledge, you have to understand what these things refer to in reality. For example you would describe t as that thing that a clock measures and apply the label "proper time". But this is an abstraction. That label covers up a hole in your understanding. There is no real thing called proper literally time flowing through the inside of a clock. Instead a clock is a device in which some kind of regular cyclic motion is used to give a cumulative display that we call the time.

77. Originally Posted by Farsight
With respect Markus, mathematical exercises will not plug the holes in your physics knowledge.
With all the contempt you deserve, I tell you that mathematical exercises will plug the gaping holes in your physics knowledge. You are a disgusting individual, seeking to push yourselves on others, especially those looking for real knoweldge, proud in your own ignorance. You do not understand physics because the mathematics is fundamental to the enterprise.
But what's the point? Writing down mathematical expressions for balls and planes and cones does not increase anybody's understanding of the basics. The basics are the terms, like those above, like E and p and m and c and C and h and t.
How ignorant can you be? "E and p and m and c and C and h and t" are all mathematical terms; they get their meaning only because we use them mathematically. They have their place in physics because the math that we do with them allows us to successfully model physical events. But if one cannot do the math with them, then we have no model and no use in physics.

78. Originally Posted by Farsight
For example you would describe t as that thing that a clock measures and apply the label "proper time". But this is an abstraction. That label covers up a hole in your understanding. There is no real thing called proper literally time flowing through the inside of a clock. Instead a clock is a device in which some kind of regular cyclic motion is used to give a cumulative display that we call the time.
So time is not what a clock measures. But a clock measures time. Got it.

79. Originally Posted by Farsight
With respect Markus, mathematical exercises will not plug the holes in your physics knowledge.
Did you read what I said to you ? These are exercises at the end of each chapter in a textbook. I study from textbooks, then I test my own understanding by completing the exercises provided. This is precisely what will plug the holes in my understanding. If I can't complete an exercise I know that I haven't really understood the material, so I go back over it again until I get it right. That is how you learn physics, Farsight - the hard way.

If you prefer to tackle them using mathematics, I would advise you to study the terms in mathematical expressions and attempt to relate abstraction to reality.
This is just the old "maths is not important" argument in disguise. Relating abstraction to reality will not tell you where the ball lands, only a combination of understanding and application of the laws behind its motion will.

Writing down mathematical expressions for balls and planes and cones does not increase anybody's understanding of the basics.
Neither does cherry-picking quotes off other people who did learn physics the proper way.

But what's the point?
The point is just this - while you would quote classical mechanics terms from Wikipedia and other sources, I can simply calculate exactly were the ball will hit the plane. Period. And I can calculate this because I understand the laws behind the ball's motion, and how those laws relate to the real world.
Or are you saying to us that being able to make predictions ( = calculate ) is not needed in physics ? Because to me that is exactly what you are implying by your "But what's the point?".

The basics are the terms, like those above
Yes - and you have already given us many a demonstration as to the level of your understanding - or rather lack thereof - of these terms in the Einstein equations. A thorough study of a textbook or two would certainly do you a world of good, Farsight. The same goes for me, but the difference between us is that I acknowledge my level of ignorance, and do something about it, whereas you seem to be content in believing that your supposed knowledge is somehow superior.

80. Markus: Nice work, great stuff. One small caveat.

You wrote, or rather implied, that if then are mutual inverses. This is completely correct, but be aware, as you probably are, that matrix multiplication is not in general commutative. So for arbitrary matrices .

As for your outstanding questions, I think I will start a new thread in Math - stay tuned

Farsight: You keep banging on about the difference between what you call mathematical abstraction and something you call "reality". So here's a question for you......

....who decides what is "reality" and what criteria do they use in order to come to this decision?

Careful not to invoke "common sense" or intuition, as you will crash in flames

81. Originally Posted by Guitarist
You wrote, or rather implied, that if then are mutual inverses. This is completely correct, but be aware, as you probably are, that matrix multiplication is not in general commutative. So for arbitrary matrices .
Oops, you are right, I completely forgot about that

As for your outstanding questions, I think I will start a new thread in Math - stay tuned
Sounds good, thank you.

82. Originally Posted by Strange
So time is not what a clock measures. But a clock measures time. Got it.
No, you haven't got it. Open a grandfather clock, see that pendulum moving? Take the back off a mechanical wristwatch. See that spring and a balance and all sort of cogs? Moving? If you had a microscope you could see the that your quartz wristwatch is driven by an oscillating crystal. It's moving. A caesium atomic clock at NIST works off the hyperfine transition and microwaves, which are moving. An optical clock at NIST is much the same but uses aluminium and visible wavelengths. Sinusoidal light waves. Moving. There's always some kind of regular cyclic motion being counted and accumulated, with some kind of display. When you open up your clock you do not see proper time flowing through it. You see things moving, and it's that simple. Clocks "clock up" local motion. That's what clocks do. Learn to put your trust in the things you can see instead of abstract things you cannot. Learn to be empirical. And before you comfort yourself with the vainglorious thought that this is just some "my theory" that I'm makling up, buy yourself a copy of A world without time: the forgotten legacy of Godel and Einstein.

83. Originally Posted by Markus Hanke
Did you read what I said to you ? These are exercises at the end of each chapter in a textbook. I study from textbooks, then I test my own understanding by completing the exercises provided. This is precisely what will plug the holes in my understanding. If I can't complete an exercise I know that I haven't really understood the material, so I go back over it again until I get it right. That is how you learn physics, Farsight - the hard way.
No it isn't. Fifty thousand people could do this for a hundred years, and they will not advance their physics knowledge one jot. To advance their physics knowledge they must understand the mathematics, and to understand the mathematics they must understand the atoms, the words of that mathematics. They must understand the terms.

Originally Posted by Markus Hanke
This is just the old "maths is not important" argument in disguise.
No it isn't. Don't kid yourself. You cannot understand that mathematics if you do not know what those terms really mean. If you do not, you doom yourself to going round in circles forever.

Originally Posted by Markus Hanke
Relating abstraction to reality will not tell you where the ball lands, only a combination of understanding and application of the laws behind its motion will.
Don't give me laws Markus. We do physics to understand the world, and we do not settle for because that's the law.

Originally Posted by Markus Hanke
Neither does cherry-picking quotes off other people who did learn physics the proper way.
Dismiss Einstein at your peril. I'm with Einstein on all this. Where does that leave you?

Originally Posted by Markus Hanke
The point is just this - while you would quote classical mechanics terms from Wikipedia and other sources, I can simply calculate exactly were the ball will hit the plane. Period. And I can calculate this because I understand the laws behind the ball's motion, and how those laws relate to the real world.
There are no laws. The real world is what it is. And it is chock full of symmetry, only this thread is gravity/mass and you do not understand the symmetry between momentum and inertia.

Originally Posted by Markus Hanke
Or are you saying to us that being able to make predictions ( = calculate ) is not needed in physics ? Because to me that is exactly what you are implying by your "But what's the point?".
No. Don't put words into my mouth. I'm on record as saying that mathematics is a vital tool for physics. To understand that physics you have to understand that mathematics. And to understand that mathematics you don't have to be adept at using it, you have to understand the terms.

Originally Posted by Markus Hanke
Yes - and you have already given us many a demonstration as to the level of your understanding - or rather lack thereof - of these terms in the Einstein equations. A thorough study of a textbook or two would certainly do you a world of good, Farsight. The same goes for me, but the difference between us is that I acknowledge my level of ignorance
Oh no you do not. I'm forever putting you straight, with never a word of thanks. It's called hubris Markus. Look it up. And look in the mirror, like I looked int he mirror six years ago.

Originally Posted by Markus Hanke
and do something about it, whereas you seem to be content in believing that your supposed knowledge is somehow superior.
I've done something about it. You're just going round in circles, lost in a desert of abstraction, defining terms only in terms of other terms, and never getting to the bottom of anything. You are physics in a microcosm, and it's withering on the vine. Not on my watch Markus. Not on my watch.

84. Proper time is the interval between two events in space-time, as measured along a world-line that intersects those two events. That's the simplest definition I can think of for it.

A clock carried along a world-line measures proper time. A light-clock would be the ideal solution.

All clocks carry proper time with them along their world-lines. It matters not what external forces do to their world-lines, a (light) clock always measures proper time.

85. Originally Posted by Guitarist
Farsight: You keep banging on about the difference between what you call mathematical abstraction and something you call "reality". So here's a question for you......

....who decides what is "reality" and what criteria do they use in order to come to this decision?

Careful not to invoke "common sense" or intuition, as you will crash in flames
Observers decide, using the empirical evidence of what they can see supported by theory and mathematics and prediction and test. And when they find that their observations do not tally, they compare notes in order to understand why, and thence understand the deeper reality, and why your motion through the world alters the way that you see it. Or not, as the case may be. Move fast through the universe, and distance and time appears to change. But in your box, nothing changes at all.

86. Originally Posted by SpeedFreek
Proper time is the interval between two events in space-time, as measured along a world-line that intersects those two events. That's the simplest definition I can think of for it. A clock carried along a world-line measures proper time. A light-clock would be the ideal solution. All clocks carry proper time with them along their world-lines. It matters not what external forces do to their world-lines, a (light) clock always measures proper time.
I'm sorry SpeedFreek, but a world-line is an abstract thing in an abstract mathematical space called spacetime. Can you point up to the clear night sky and point out a worldline? No. Can you take the back off a clock and point to the proper time flowing through it? No. And as Strange now understands, there is no motion in spacetime. It's a static "all-times-view" mathematical model of motion through space over time, wherein proper time is merely a cumulative measure of local motion and nothing more. In no sense do clocks literally carry proper time along their world lines. They don't move along their world lines, they move through space. And if they don't, the only motion is the motion of things inside those clocks. Through space. And in a light clock, the thing that moves is light. Through space. This is it guys, this is empiricism. This is 21st century physics. It's Einstein's physics too, and you can't explain where it's wrong. Because it isn't. That's why it's coming soon to a university near you. And it's time you started getting used to it.

87. Originally Posted by Farsight
In no sense do clocks literally carry proper time along their world lines. They don't move along their world lines, they move through space.
Over time. You can't have movement without time. They move through space and time. Their path through space and time is known as their world-line.

Originally Posted by Farsight
And if they don't, the only motion is the motion of things inside those clocks. Through space.
Over time. Do try to listen. You keep missing time out of the equation. It's like a blind spot or something.

Originally Posted by Farsight
And in a light clock, the thing that moves is light. Through space.
Over time.

Originally Posted by Farsight
This is it guys, this is empiricism.
We empirically measure things to move through space, over time. It is pretty difficult to define velocity without it.

88. Originally Posted by Farsight
No it isn't. Fifty thousand people could do this for a hundred years, and they will not advance their physics knowledge one jot. To advance their physics knowledge they must understand the mathematics, and to understand the mathematics they must understand the atoms, the words of that mathematics. They must understand the terms.

So you are saying that there have been no advances in physics in the last 200 years or so ? Because the above is how you learn physics at university/college.
You cannot advance anything unless you first understand it from the ground up. In order to do that you need to put in the effort to study first. It is hard for me to believe that you argue with that.

No it isn't. Don't kid yourself. You cannot understand that mathematics if you do not know what those terms really mean. If you do not, you doom yourself to going round in circles forever.
Yes, we know that. Mathematics is the language, physics is the subject matter. You need to know both for a full understanding, that is precisely why one needs to initially sit down and study.

Don't give me laws Markus. We do physics to understand the world, and we do not settle for because that's the law.
You are deliberately misunderstanding me. What we are settling for is the exact prediction of where the balls lands, each and every time, under any scenario. And that can only happen once we understand why the ball lands where it lands.

Dismiss Einstein at your peril. I'm with Einstein on all this. Where does that leave you?
It leaves me here :

General Proof that Special Relativity is Self-Consistent
Solving the Einstein Field Equations

The reader can form his/her own opinion who is with Einstein and who is not.

There are no laws. The real world is what it is. And it is chock full of symmetry, only this thread is gravity/mass and you do not understand the symmetry between momentum and inertia.
Ever heard of Noether's theorem ? *(desparate scramble for Wikipedia...)*

Oh no you do not. I'm forever putting you straight, with never a word of thanks. It's called hubris Markus. Look it up. And look in the mirror, like I looked int he mirror six years ago.
That only means you wasted six years, because you didn't really see.

You're just going round in circles
Sad that you see it that way. But regardless, I can see that I won't be changing your mind; we all make our choices, you have made yours and I have made mine. My choice was to put in the work to better myself, what yours is I shall never really know.

89. Originally Posted by Farsight
Can you point up to the clear night sky and point out a worldline? No.
Can you point up to the clear night sky and point out inhomogeneous space ? No.
Seems like inhomogeneous space is an abstract thing in an abstract mathematical space.
I wonder where that leaves us...

90. I'm forever putting you straight, with never a word of thanks.
I am beginning to understand now that you really believe this; if so you are probably too far gone already to be helped.

91. Originally Posted by Farsight
And as Strange now understands ....
Please drop the condescending, "I have explained and now you know The Truth" attitude. Much of what you write is risible (such as your child-like clock analogy). The more you post, the more I move towards assuming anything you say is probably wrong.

92. Originally Posted by SpeedFreek
Originally Posted by Farsight
In no sense do clocks literally carry proper time along their world lines. They don't move along their world lines, they move through space.
Over time. You can't have movement without time. They move through space and time. Their path through space and time is known as their world-line.
No they don't move through time at all. That's just a figure of speech. Can you literally see those cogs and gears moving through time. How about if we stop the clock? Those cogs and gears are now motionless. But what, they're still moving are they? Let's see now, light is moving from them to your eye. Inside your head electrochemical signals are going from one neuron to another. They're moving. The pendulum clock behind you is moving too. And the Earth, and the Sun, and so on. But where is this thing called time they're moving through? Can you see it? No. Let's stop that light moving, and the electrochemical signals in your brain, and everything else. Where's your moving through time now? Nowhere. So please recognise a figure of speech for what it is, and don't fool yourself that this is some my-theory thing I'm making up. Go and buy A world without time: the forgotten legacy of Godel and Einstein.

Originally Posted by SpeedFreek
Over time. Do try to listen. You keep missing time out of the equation. It's like a blind spot or something.
I haven't got the blind spot. Take another look at clocks carry proper time along their world lines. What kind of fantasy is that? Do you think of a stopped clock as something bent over with a heavy parcel as it shins up some pole called a worldline? Do not let such abstractions cloud your vision of what a clock really does.

Originally Posted by SpeedFreek
We empirically measure things to move through space, over time. It is pretty difficult to define velocity without it.
And how do you define the second and the metre? Using the motion of light. Now pay attention, because this is important. Look at the NIST caesium fountain clock, and look at the definition of the second: "Since 1967, the second has been defined to be the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. This definition refers to a caesium atom at rest at a temperature of 0 K (absolute zero), and with appropriate corrections for gravitational time dilation." In that NIST clock, lasers and a microwave cavity are employed to cause hyperfine transitions, which are electron spin-flips within caesium atoms. The hyperfine transition emits microwaves, which is light in the wider sense. There’s a peak frequency in that emitted light, which is found and measured by the detector. But note that frequency is measured in Hertz, which is defined as cycles per second, and the second isn't defined yet. So what the detectors really do, is count the incoming microwave peaks. When they get to 9,192,631,770, that's a second. The frequency is 9,192,631,770 Hertz by definition. Now look at the metre. It's "the length of the path travelled by light in vacuum during a time interval of 1/299,792,458 of a second." Has the penny dropped yet? We use the motion of light to define the metre and the second, and we then use them to say how fast something is moving. All we're ever doing is saying how fast it's moving compared to the motion of light. Sit down and think it through. Be empirical. It isn't you need time to have motion. It's the other way round. You need motion to have time. That's what Godel and Einstein worked out in 1949.

93. Originally Posted by Markus Hanke
So you are saying that there have been no advances in physics in the last 200 years or so ? Because the above is how you learn physics at university/college.
You cannot advance anything unless you first understand it from the ground up. In order to do that you need to put in the effort to study first. It is hard for me to believe that you argue with that.
Don't put words into my mouth. Read what I said instead of being dismissive. From the ground up means you study those terms. Without that you haven't started from the ground up, you're building castles in the air.

Originally Posted by Markus Hanke
Yes, we know that. Mathematics is the language, physics is the subject matter. You need to know both for a full understanding, that is precisely why one needs to initially sit down and study.
And you don't understand that mathematics if you don't understand those terms. You don't know what m is, Markus. People like you peddle the mystery of mass even though Einstien explained it over a hundred years ago.
Originally Posted by Markus Hanke
Re: Don't give me laws Markus. We do physics to understand the world, and we do not settle for because that's the law.]You are deliberately misunderstanding me. What we are settling for is the exact prediction of where the balls lands, each and every time, under any scenario. And that can only happen once we understand why the ball lands where it lands.
I don't think you understand why the ball lands at all. Would you care to start a thread called Why a ball falls down and try to demonstrate to me that you understand it?
Originally Posted by Markus Hanke
It leaves you lost in abstraction, unaware of why the line element measuring the distance between two events in space-time is the same for all observers. And I venture to suggest that despite all that impressive mathematical symbology, you cannot explain why that ball falls down. You do not really understand something unless you can explain it to your grandmother. Can you Markus? Do you even dare to try?

Originally Posted by Markus Hanke
The reader can form his/her own opinion who is with Einstein and who is not.
Yes, they can, and every time you airily dismiss what the guy said as "cherry picking", they can see that he's with me.

Originally Posted by Markus Hanke
Ever heard of Noether's theorem ? *(desparate scramble for Wikipedia...)*
Of course I have. Don't try cheap shots, they cheapen you not me.

Originally Posted by Markus Hanke
That only means you wasted six years, because you didn't really see.
I haven't wasted my time Markus.

Originally Posted by Markus Hanke
Sad that you see it that way. But regardless, I can see that I won't be changing your mind; we all make our choices, you have made yours and I have made mine. My choice was to put in the work to better myself, what yours is I shall never really know.
Wait and see.

Originally Posted by Markus Hanke
Can you point up to the clear night sky and point out inhomogeneous space ? No.
Yes. I can point to the space around the moon, and I'm pointing to inhomogeneous space.

Originally Posted by Markus Hanke
Seems like inhomogeneous space is an abstract thing in an abstract mathematical space.
Not if you read what Einstein said it isn't.

"the recognition of the fact that “empty space” in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gμν), has, I think, finally disposed of the view that space is physically empty."

Originally Posted by Markus Hanke
I wonder where that leaves us...
It leaves Einstein with me, and you on a limb.

Originally Posted by Markus Hanke
I am beginning to understand now that you really believe this; if so you are probably too far gone already to be helped.
Whatever gives you comfort Markus. Now start that thread. Explain it to your grandmother if you dare.

94. Originally Posted by Strange
Please drop the condescending, "I have explained and now you know The Truth" attitude. Much of what you write is risible (such as your child-like clock analogy). The more you post, the more I move towards assuming anything you say is probably wrong.
Well that's one way to dismiss empirical evidence. Shall we try again? Open a grandfather clock, see that pendulum moving? Take the back off a mechanical wristwatch. See that spring and a balance and all sort of cogs? Moving? If you had a microscope you could see the that your quartz wristwatch is driven by an oscillating crystal. It's moving. A caesium atomic clock at NIST works off the hyperfine transition and microwaves, which are moving. An optical clock at NIST is much the same but uses aluminium and visible wavelengths. Sinusoidal light waves. Moving. There's always some kind of regular cyclic motion being counted and accumulated, with some kind of display. When you open up your clock you do not see proper time flowing through it. You see things moving, and it's that simple. Clocks "clock up" local motion. That's what clocks do. Would you care to offer a carefully thought-out rebuttal replete with your own empirical evidence? One that justifies all that proper time flowing through the clock like some mystic river? No? Didn't think so.

95. Originally Posted by Farsight
Shall we try again?
"If I can't see it, it doesn't exist. So there." But, amazingly, with his Far Sight powers he can see inhomogeneous space and sinusoidal light waves moving.

I understand the username now: you can see further than others without needing to stand on anyone's shoulders.

96. Another useless wisecrack instead of empirical physics. The username was one I adopted when share trading in about 2002.

97. Originally Posted by Farsight
Another useless wisecrack instead of empirical physics..
Like you preferring random quotes to demonstrating that the gravitation due to the gravitational field predicts the observed rotation curves.

98. Originally Posted by Farsight
This {complete nonsense} is 21st century physics..........That's why it's coming soon to a university near you. And it's time you started getting used to it.
Well, well, I have seen arrogant fools here and elsewhere, but nothing to compare with this TOWERING arrogance.

Moderator note Poster Farsight has been multiply corrected by real physicists, and also by those who are extremely intelligent and have an interest in physics, despite themselves having no formal background in the subject. It goes without saying, I assume, that Farsight is neither intelligent nor has he any formal training in physics

I urge casual readers not to pay any heed to his weirdo ideas

99. Care to point out where I've been corrected Guitarist? I've just looked back through the thread and the only thing I can see is a very minor strictly speaking only rank-2 tensors. What stands out instead is where I've corrected you. Take a look at posts 16, 32, 39, 46, 49, 51. And your emotional response is abuse I'm afraid, and you are further abusing your position as a moderator by permitting abuse instead of empirical phyiscs. Thanks for offering me the moral high ground, I'll take it thanks. Oh, and by the way I really do talk about 21st century physics. I stay abreast of current developments instead of treating some fifty-year old textbook like a bible. You should too.

Now, does anybody want to talk about gravity and mass?

100. Originally Posted by Farsight
No they don't move through time at all. That's just a figure of speech.
It seems you fail to understand words, so here are some pictures.

Perhaps a Penrose spacetime diagram (for Minkowski spacetime) will help you.

Notice the path of the photon ray?

Here is another spacetime diagram for you, showing the world line of an accelerating observer.

In this animation, the vertical direction indicates time and the horizontal direction indicates distance, the dashed line is the spacetime trajectory ("world line") of an accelerating observer. The small dots are arbitrary events in spacetime that are stationary relative to each other. The events passing the two diagonal lines in the lower half of the picture (the past light cone of the observer) are those that are visible to the observer.

The slope of the world line (deviation from being vertical) gives the relative velocity to the observer. Note how the view of spacetime changes when the observer accelerates. In particular, absolute time is a concept not applicable in Lorentzian spacetime: events move up-and-down in the figure depending on the acceleration of the observer.

101. I'm familiar with the above, SpeedFreek. The gif lower down is badly misleading because it suggests that there is motion through spacetime. There isn't. You can emulate spacetime with a movie camera. You film something, such as a red ball, then cut the film into individual frames, and form them into the block. The red streak in the block is the worldline of the ball. But it isn't actually moving up that worldline. I really am not kidding you about this. The notion that things move through spacetime is one of those physics myths that has grown up over the years. Another one is that a ball falls down because the spacetime in the room you're in is curved. That isn't the case. Spacetime curvature is synonymous with the Riemann curvature tensor, which is in turn associated with tidal force. There's no detectable tidal force in the room you're in, but you can readily detect that ball falling down.

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