SoAMadDeathWish

Highly Advanced General Relativity for the Layman 101

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Part 5: From Newtonian Space and Time to Special Relativity.

http://www.mediafire.com/view/89xkq785010t92f/Part_5_Newtonian_Spacetime.pdf

No, No, No .... Newtonian Physics is not Lorentz invariant nor is the space of Newton the right shape.

Newtonian Mechanics assumes space is flat, infinite and independent of time. In short, it is Wrong. But it is close enough to be of use.

Ba'al Chatzaf

Where does it say that Newtonian Physics is Lorentz invariant? It is only invariant under Galilean transformations.

Which makes it wrong. The world is NOT Galilean Invariant. Nor is space flat (at least locally). Newtonian Mechanics assumes space is infinite and flat and that time is absolute. Neither is the case.

Einstein's genius move was to make mechanics consistent with Maxwell's electrodynamics which is Lorentzian out of the box.

It is amazing that the Lorentz Transform leaves much of Newtonian mechanics intact.

Ba'al Chatzaf

Uhh... yeah... I know. Where did I say otherwise?

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Part 5: From Newtonian Space and Time to Special Relativity.

http://www.mediafire.com/view/89xkq785010t92f/Part_5_Newtonian_Spacetime.pdf

No, No, No .... Newtonian Physics is not Lorentz invariant nor is the space of Newton the right shape.

Newtonian Mechanics assumes space is flat, infinite and independent of time. In short, it is Wrong. But it is close enough to be of use.

Ba'al Chatzaf

Where does it say that Newtonian Physics is Lorentz invariant? It is only invariant under Galilean transformations.

Which makes it wrong. The world is NOT Galilean Invariant. Nor is space flat (at least locally). Newtonian Mechanics assumes space is infinite and flat and that time is absolute. Neither is the case.

Einstein's genius move was to make mechanics consistent with Maxwell's electrodynamics which is Lorentzian out of the box.

It is amazing that the Lorentz Transform leaves much of Newtonian mechanics intact.

Ba'al Chatzaf

Uhh... yeah... I know. Where did I say otherwise?

One cannot correctly infer relativity theory from Newtonian Mechanics. It cannot be done.

Ba'al Chatzaf

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One cannot correctly infer relativity theory from Newtonian Mechanics. It cannot be done.

Ba'al Chatzaf

I'm not trying to. What I want to do is to eventually contrast Newtonian physics with special and general relativity in order to show that general relativity is actually a much simpler theory.

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Can someone explain this to me, a thought "experiment" I came up with after listening to a lecture on relativity:

So (and I dont have the exact quote) I remember Einstein saying something about, if he traveled on a light beam, he would still observe other light beams traveling at c instead of at rest relative to his own speed and position.

But if thats the case....

if we have a race from Mars to Neptune. Two racers, each on their own light beams and a referee/observer who starts the race and judges who won (by what ever means... maybe to judges, one at the start and one at the finish line) 3,2,1 go....

Racer A, though traveling at c, would observe Racer B blow pass him at c and thus win the race. At the same time, Racer B sees Racer A blow pass him at c and thus in his experience, A wins the race,....At the SAME TIME the referee judges the race a tie because from his position, both racers are moving at the same speed and they both arrive at the finish line at the same time..............................................................................................................??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????

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Can someone explain this to me, a thought "experiment" I came up with after listening to a lecture on relativity:

So (and I dont have the exact quote) I remember Einstein saying something about, if he traveled on a light beam, he would still observe other light beams traveling at c instead of at rest relative to his own speed and position.

But if thats the case....

if we have a race from Mars to Neptune. Two racers, each on their own light beams and a referee/observer who starts the race and judges who won (by what ever means... maybe to judges, one at the start and one at the finish line) 3,2,1 go....

Racer A, though traveling at c, would observe Racer B blow pass him at c and thus win the race. At the same time, Racer B sees Racer A blow pass him at c and thus in his experience, A wins the race,....At the SAME TIME the referee judges the race a tie because from his position, both racers are moving at the same speed and they both arrive at the finish line at the same time..............................................................................................................??????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????

One very important thing, no observer can ever travel at the speed of light.

We can, however, consider the same scenario if both observers are traveling at very nearly the speed of light.

First of all, we always have to define the reference frames. One possible frame here is the Mars-Neptune frame, in which Mars and Neptune are at rest. The other two frames are that of each of the racers. Supposing that they start off an equal distance from Neptune, and leave at the same time and place in the Mars-Neptune frame, and so long as they travel at the same near-light speed speed, they will finish at the same time in the Mars-Neptune frame. Since they are traveling with the same speed, the two racers are at rest relative to each other in their frame, while Neptune is approaching them at very nearly the speed of light. In that frame, they still both observe that Neptune reaches them at the same time.

However, your thought experiment is a clever demonstration of why it is impossible to have observers at light speed.

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We can, however, consider the same scenario if both observers are traveling at very nearly the speed of light.

but didnt Eisnteins thought experiment begin with him moving AT the speed of light while looking at himself in the mirror?? We arent asking whenther IF IT IS possible, but rather, IF IT WAS possible what would we observe.

Secondly, I could see that both racers would observe they arrive at the same time if they are observing Neptune, but my thought is that they are observing EACH OTHER while they travel

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We can, however, consider the same scenario if both observers are traveling at very nearly the speed of light.

but didnt Eisnteins thought experiment begin with him moving AT the speed of light while looking at himself in the mirror?? We arent asking whenther IF IT IS possible, but rather, IF IT WAS possible what would we observe.

In special relativity, it is impossible to even consider what would happen if an observer moved at the speed of light, because that would contradict the first postulate.

If by "an observer traveling at the speed of light" we mean an inertial observer for which all light is at rest (in a given direction), then it would be impossible for him to measure time in places that are behind him, because the light from those clocks would never reach him. He therefore cannot be an inertial observer.

I think Einstein's thought experiment that you're talking about was about the ether theory. In that theory, the first postulate of special relativity did not hold, so one could sensibly ask what would happen if one traveled at the speed of light. However, since such a theory assumes an absolute time, they would still arrive at the same time on Neptune in all frames, anyway.

Secondly, I could see that both racers would observe they arrive at the same time if they are observing Neptune, but my thought is that they are observing EACH OTHER while they travel

Since they are traveling at the same speed and in the same direction, when each racer looks at the other, he observes that the other guy is not moving at all.

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Death Wish,

Just use tensorial calculus and talk about what you are trying to do. It's not like it's only used in General Relativity. Tensor Matrices are extensively used in Materials Engineering and other technical disciplines. Trust me, plenty of people here can handle that kind of math more easily than a presentation of functional topology from first principles or maybe I'm not "highly advanced" enough, LOL.

Jim

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Death Wish,

Just use tensorial calculus and talk about what you are trying to do. It's not like it's only used in General Relativity. Tensor Matrices are extensively used in Materials Engineering and other technical disciplines. Trust me, plenty of people here can handle that kind of math more easily than a presentation of functional topology from first principles or maybe I'm not "highly advanced" enough, LOL.

Jim

In structural engineering 3 d and 6 d tensors are used a lot. In relativity 4 d tensors are used since the space time manifold is a semi-Riemannian manifold. General n-tensors were developed by Bernhard Riemann to talk about many different kinds of "smooth" geometric spaces of all dimensions.

See

http://people.mpim-bonn.mpg.de/hwbllmnn/archiv/dg2srm02.pdf

http://www.math.harvard.edu/~shlomo/docs/semi_riemannian_geometry.pdf

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Thanks Bob, much better. Why is it that so many people want to avoid mathematical formalism? It makes things easier. Even if the subject is hard, there's no way to get around it.

Jim

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Thanks Bob, much better. Why is it that so many people want to avoid mathematical formalism? It makes things easier. Even if the subject is hard, there's no way to get around it.

Jim

No math, no physics. No math, very little engineering.

Mathematics will not tell us the nature of the cosmos but without it we will know very little about the cosmos.

An interesting thing to note: Before about 500 years ago, the smartest people in the world did not have the means to really understand the physical world. The managed with rough empirical methods but to get to the reality behind the appearances they first had to develop the mathematics.

Ba'al Chatzaf

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Death wish,

Sorry to be responding so late, and sorry to keep beating a dead horse but you answers have not been satisfying yet... Perhaps it is because I do not have a clear understanding of the premise. So let me ask, does or does the the theory not state that light travels at c regardless of the observers relative speed and/or position? Yes or no

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Death wish,

Sorry to be responding so late, and sorry to keep beating a dead horse but you answers have not been satisfying yet... Perhaps it is because I do not have a clear understanding of the premise. So let me ask, does or does the the theory not state that light travels at c regardless of the observers relative speed and/or position? Yes or no

It does.

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Then if a (hypothetical) observer was moving at c, then they would still observer light moving away from them at exactly c?

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Then if a (hypothetical) observer was moving at c, then they would still observer light moving away from them at exactly c?

When talking about motion, it's always a good idea to ask what the observer is supposed to be moving relative to. Every observer is always at rest in his own inertial frame. If you say that an observer is moving with some velocity v, then you must specify the frame he is moving relative to as well.

Also, there are no such things as inertial observers that move with velocity c with respect to any other inertial frame. As I've said before, such an observer would not be able to read the clocks in his own frame, which is a serious problem.

We can, however, talk about an observer that is moving with a velocity close to c with respect to a second observer. In that case, both observers would measure any light moving away from them at exactly c.

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Okay so the observer is moving and c relative to his home in Baltimore MD. He should still observer light moving at c relative to his interia right?

I don't understand why you keep saying someone moving at near c, this is a thought experiment, the same as the one that got Einstein thinking about the theory in the first place.

Maybe I just need someone to sit down with...

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I have a "better" example. Suppose I leave from home traveling at 99.99 c. Friends at home would see my speed as 99.99 c relative to Baltimore, heading toward Saturn. I then shine a super flashlight onto my destination (while in flight). I observe it illuminate Saturn, before I get there because regardless of my speed, light leaves my flashlight at c and thus I can verify it reaches there first by the light reflecting back (also traveling at c relative to me). What do friends on earth see? Using a telescope, do they also see the light reach the destination before me, which means it would be going two or three times my speed in order to reach and reflect, or do they see us (the light and me) arrive at very nearly the same time?

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I have a "better" example. Suppose I leave from home traveling at 99.99 c. Friends at home would see my speed as 99.99 c relative to Baltimore, heading toward Saturn. I then shine a super flashlight onto my destination (while in flight). I observe it illuminate Saturn, before I get there because regardless of my speed, light leaves my flashlight at c and thus I can verify it reaches there first by the light reflecting back (also traveling at c relative to me). What do friends on earth see? Using a telescope, do they also see the light reach the destination before me, which means it would be going two or three times my speed in order to reach and reflect, or do they see us (the light and me) arrive at very nearly the same time?

Light travels at the same speed in all inertial frames of reference.

Suppose you flashed a light back to earth at the same time you flashed a light on the planet which in turn reflected back to earth. The observer on earth would see the backward flash you made before he saw the light reflected off the planet.

Ba'al Chatzaf

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Baal, that doesn't answer my question, but I'm glad you've joined the conversation. Maybe you can help.

My "better" example was made based on my first question which I posed in the last page of this thread. The paradoxical nature of that question is what I am trying to understand

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I have a "better" example. Suppose I leave from home traveling at 99.99 c. Friends at home would see my speed as 99.99 c relative to Baltimore, heading toward Saturn. I then shine a super flashlight onto my destination (while in flight). I observe it illuminate Saturn, before I get there because regardless of my speed, light leaves my flashlight at c and thus I can verify it reaches there first by the light reflecting back (also traveling at c relative to me). What do friends on earth see? Using a telescope, do they also see the light reach the destination before me, which means it would be going two or three times my speed in order to reach and reflect, or do they see us (the light and me) arrive at very nearly the same time?

Short answer: Both you and the people on Earth observe that the light reached Saturn first. But the people on Earth observe that the light took less time to reach Saturn after you shined it.

Long answer:

Let's say that the distance between Earth and Saturn is d (in the Earth frame) and that at the halfway point on your journey to Saturn, you shine a light at Saturn. The distance that light travels is d/2, and so it takes d/(2c) seconds for the light to go from you to Saturn in the Earth frame.

But in your frame, the distance between Earth and Saturn is not d, but rather d*Sqrt(1 - (v^2)/(c^2)) (because of length contraction), which turns out to be d*0.0141421 when your velocity is 99.99% of c. The halfway point of your journey is at half this distance, so you shine the light at d*0.00707105. That means that the light arrives at Saturn after d/(0.00707105*c) seconds in your frame (because of time dilation).

d/(2c) < d/(0.00707105*c)

but

d > d*0.0141421

So in the Earth frame, the light traveled a longer distance, but it took less time to get there. Whereas in your frame, it traveled a shorter distance, but it also took a longer time to get there. Thus, light never goes "two or three times your speed" to reach Saturn. Light always travels at c, it is never ever slower or faster across inertial frames. Instead, space and time contract and dilate.

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Part 6 is finally up. The reason it took so long is because a) I've been busy, and b) it took me quite a while to think of an approach that would explain the core concepts of SR while sidestepping all of the rather unnecessary usual algebraic baggage.

http://www.mediafire.com/view/z035cgg5iscwkpx/Part_6_Special_Relativity.pdf

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Part 6 is finally up. The reason it took so long is because a) I've been busy, and b) it took me quite a while to think of an approach that would explain the core concepts of SR while sidestepping all of the rather unnecessary usual algebraic baggage.

http://www.mediafire.com/view/z035cgg5iscwkpx/Part_6_Special_Relativity.pdf

This short and sweet coverage of general relativity is hard to beat.

http://preposterousuniverse.com/grnotes/grtinypdf.pdf

Ba'al Chatzaf

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Currently reading

Einstein's Theories of Relativity and Gravitation by J. Malcolm Bird

It is about a competition that was held to see who could explain relativity to the general population in 3000 words or less. I'm about half way through it and there has only been about 3 mathematical statements and they have been used purely as analogies. I'm loving the book so far. It explains everything very systematically starting with how humans think (Greek philosophers) and each chapter builds on the next where, in plain English, you almost have no choice but to agree with ALL of the conclusions.

It is available to read for free online

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You cannot really describe a differentiable manifold using just words. Math is necessary because a manifold IS a mathematical object.

Challenge accepted.

I see you have attempted to deal with topological spaces with "no math". Now with what you have prove

the Tychonoff Compactness Theorem. Or prove the Jordan Curve Theorem with a no-math approach. I would really like to see that done.

This is about physics, not topology.

The exoskeleton of physics is mathematics. Without math you do not have modern physics.

Math is more that a supporting structure for physics. It is in the DNA of physics. Example: The Noether Theorem which sets up a correspondence between the group symmetries in physical laws and the conservation laws of physics. The best known correspondences are the conservation of angular momentum and the isotropic nature of space. If God had created the cosmos turn at an angle of 15.546789 degrees from its current orientation the laws of physics would still be the same. The correspondence between translation invariance and the conservation of linear momentum. If God had created the universe moved 17.66598888 yards to the left of where it is, the laws of physics would still be the same. The correspondence between time displacement and the conservation of energy. If God had made the cosmos 2.0005558 seconds sooner the laws of physics would still be the same. You will notices the correspondences are the same as shows up in the Heisenberg Uncertainty Principle. Angle-and angular momentum. Length and linear momentum Time and Energy This is important in quantum theory.

I was being a bit whimsical but I do hope you get the idea. The conservation of certain quantities and the invariance of physical laws under a set of group transformation (aka symmetries) indicates that our -physical- conservation laws are totally intertwined with mathematical symmetries in the physical laws. In short, you can't separate the math and the physics.

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