Compton Wavelength

[Farsight]

...Light doesn't curve because a gravitational field is there, it curves because the space down there isn't the same as the space up here. The potential is just a cipher for the state of space.

...and just like this, this forum reaches an all time low.

Take that one up with Einstein, Tach. I've highlighted a few words for your convenience:

"...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)...",

It does contribute to the gravitational mass of the clock.

...and the records for BS keep getting toppled.

The gravitational potential energy you give to the clock by raising it does contribute to its gravitational mass. Go and read up about the mass defect, binding energy, and conservation of energy. Then if you're still not clear, come back to me and I'll explain it to you.

 

[prometheus]

Take that one up with Einstein, Tach. I've highlighted a few words for your convenience:

"...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)...",

We've had this discussion before but I'm going to ask again because I didn't get a satisfactory answer last time: Given that the metric is a symmetric, rank 2 tensor, and it contains 10 independent functions, what is it's dimension? In the case of the metric, this is the dimension of the manifold it describes, or in other words the dimensions of the space. To make it super easy for you, the number of independant components in a rank 2 symmetric tensor is $$\frac{1}{2} d (d+1)$$, so was Einstein talking about the spatial components of spacetime, or spacetime?

 

[Farsight]

So where is all this done? You realise you can't just take any math and say it should be interpreted a certain way, right? You've got to be able to show that you can recover that math from your interpretation of it. It's not like electromagnetism is trivially equivalent to anything you've said. I know the mathematics of electromagnetism, and I know the mathematics of curved spaces, and they're not the same. So where do you or any of the people you've named make the connection? What are the models behind the buzzwords you're using, and how do you derive or recover the mathematics of electrodynamics from those models?

Sorry pryzk, I can't show you some root-and-branch development of electromagnetism. But I'll have a dig around for something by somebody that numerically predict any of the usual, routine predictions of electromagnetism.

Er, no, curl is just the name of an operator in vector calculus, and we'll say a vector field $$\bar{F}$$ has curl if $$\bar{\nabla} \times \bar{F} \neq 0$$. The reason the operator is called "curl" isn't random of course, but it's got nothing to do with space being curved or twisted or anthing like that. Water stirred in a glass has curl (or more correctly, it's local velocity does) by the vector calculus definition, for example.

Yes, and "curl (or rotor) is a vector operator that describes the infinitesimal rotation of a 3-dimensional vector field". I said take it at face value, look at rotor, look at gravitomagnetism. Make the connection.

 

[RJBeery]

Go and read up about the mass defect, binding energy, and conservation of energy. Then if you're still not clear, come back to me and I'll explain it to you.

Make the connection.

Farsight, I think comments like this are hilarious when directed at "certain people". However, if you're looking for sincere participation I think some people might find it a bit condescending, which starts to involve egos. I am certainly guilty of this myself (so feel free to point it out!), but lately I've tried to pique intellectual curiosity in a passive way rather than announce that I have all the answers.

 

[Farsight]

Noted RJ. I did mean to be sincere, and if I come over as condescending I can only apologise and resolve to check what I post before I hit the ENTER key.

 

[rpenner]

That's not taking it at face value. That's making up stories.

Curl is a differential operator that works on smooth vector fields in 3-dimensional spaces. It says nothing about the space being curved or twisted -- it can talk only about the vector field.

Curl (or rotor) is not something that you can make up stories about. It's a mathematical concept with a rigorous definition and therefore requires mathematical development to demonstrate claims about it are true.

Here's a simple example of how to apply curl to a nearly trivial case. There is a slight abuse of notation which avoids having memorize ugly rules or introduce more mathematical notation.
$$\textrm{curl} \, \begin{pmatrix} -y \\ x \\ 0 \end{pmatrix} = \left| \begin{pmatrix} \hat{x} & \hat{y} & \hat{x} \\ \frac{\partial \quad}{\partial x} & \frac{\partial \quad}{\partial y} & \frac{\partial \quad}{\partial z} \\ -y & x & 0 \end{pmatrix} \right| = \left| \begin{pmatrix} \frac{\partial \quad}{\partial y} & \frac{\partial \quad}{\partial z} \\ x & 0 \end{pmatrix} \right| \hat{x} - \left| \begin{pmatrix} \frac{\partial \quad}{\partial x} & \frac{\partial \quad}{\partial z} \\ -y & 0 \end{pmatrix} \right| \hat{y} + \left| \begin{pmatrix} \frac{\partial \quad}{\partial x} & \frac{\partial \quad}{\partial y} \\ -y & x \end{pmatrix} \right| \hat{z} = \left( \frac{\partial \quad}{\partial x} x - \frac{\partial \quad}{\partial y} (-y) \right) \hat{z} = \begin{pmatrix} 0 \\ 0 \\ 2 \end{pmatrix}$$

Nothing is moving or rotating, it's just abstract math applied to an abstract vector field; but if the field represents a snapshot of a velocity vector field, then in a limited sense there is a connection with the instantaneous rotation of a test object inserted at any point in the field. But it does not inform about the space, just the vector field.

 

[Farsight]

"...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)..."

We've had this discussion before but I'm going to ask again because I didn't get a satisfactory answer last time: Given that the metric is a symmetric, rank 2 tensor, and it contains 10 independent functions, what is it's dimension? In the case of the metric, this is the dimension of the manifold it describes, or in other words the dimensions of the space. To make it super easy for you, the number of independant components in a rank 2 symmetric tensor is $$\frac{1}{2} d (d+1)$$, so was Einstein talking about the spatial components of spacetime, or spacetime?

There's four dimensions in the manifold, 2 * (4 + 1) = 10. We're all familiar with 3+1 dimensional spacetime, a mathematical "space". But when Einstein said space, he was talking about space space. This is clear because he talks about its metrical qualities. You measure distances and times via the motion of light through space, and you then formulate equations of motion. However there's no motion through spacetime. Have a read of the full Leyden Address and see what you make of it. There's various other sections of interest, for example:

"There can be no space nor any part of space without gravitational potentials; for these confer upon space its metrical qualities, without which it cannot be imagined at all. The existence of the gravitational field is inseparably bound up with the existence of space".

 

[Guest254]

Yes, and "curl (or rotor) is a vector operator that describes the infinitesimal rotation of a 3-dimensional vector field". I said take it at face value, look at rotor, look at gravitomagnetism. Make the connection.

Use Cartesian coordinates (x,y,z). Working on r²=x²+y²>0 we introduce the vector field

$$ \mathbf{V}= -\frac{y}{r^2} \mathbf{e}_x + \frac{x}{r^2} \mathbf{e}_y + 0\, \mathbf{e}_z $$

The integral curves of this vector field defined by

$$ \dot{x} = -\frac{y}{r^2}, \quad \dot{y}= \frac{x}{r^2}, \quad \dot{z}=0. $$

If we multiply the first by x, the second by y and add the resulting equations we deduce that the integral curves are described by

$$ x^2+y^2 = \mathrm{constant}, \quad z=\mathrm{constant}$$

i.e. little particles that moved with velocity defined by V would just rotate round the z-axis. Now compute curl(V) and show it vanishes. Now look at why we don't do physics by analogy, or mathematics by vague armwaves. Read a book, you'll get it (or possibly not).

 

[RJBeery]

Now look at why we don't do physics by analogy[...]

Making analogous connections between two systems can be a powerful tool (e.g. "let's suppose gravity is analogous to acceleration and see where this takes us"). It should be a given that it isn't the final step of anything though, and I don't think Farsight believes his analogies encompass a complete physical description.

 

[Farsight]

Quite right, RJ.

...Nothing is moving or rotating, it's just abstract math applied to an abstract vector field; but if the field represents a snapshot of a velocity vector field, then in a limited sense there is a connection with the instantaneous rotation of a test object inserted at any point in the field. But it does not inform about the space, just the vector field.

It does, rpenner. You just have to be able to see it. Get hold of a couple of magnets. Play around with them for a while - feeling the repulsion is best. Then get somebody to hold them for you whilst you waggle your hand between them. There's nothing there but air, and you know full well that you could repeat this in vacuum, in space. And you know you could put a screen between those magnets, and you won't detect any messenger particles. You won't start seeing dots on the screen caused by virtual photons. And I'll presume you don't believe in magical mysterious action-at-a-distance. So ask yourself, what is this field?

We know that a typical magnet involves electron spin, see wiki for more. And we know that a compass needle, in itself a magnet, experiences a torque in a magnetic field. Electrons affect other electrons through the intervening space. Ordinarily people say "ah, that's because of the electromagnetic field", but they don't actually ask themselves what this thing is. That's where gravitomagnetism comes in. Read this report. It starts off by saying Einstein was right again. There is a space-time vortex around Earth. It goes on to quote Clifford M Will: "One day," he predicts, "this will be written up in textbooks as one of the classic experiments in the history of physics". This is good stuff. Yes, it's written for the layman, with sentences like "Gravity, says Einstein, is simply the motion of objects following the curvaceous lines of the dimple. If Earth were stationary, that would be the end of the story. But Earth is not stationary. Our planet spins, and the spin should twist the dimple..." But it gets across the "twisted" space, the result of frame-dragging. Now take a look at the part1 title of On Physical Lines of Force. It's the theory of molecular vortices. Maxwell didn't know about electrons and spin, but he know about vortexes. Think electron spin. Make the connection.

 

[RealityCheck]

...
...

Nothing is moving or rotating, it's just abstract math applied to an abstract vector field; but if the field represents a snapshot of a velocity vector field, then in a limited sense there is a connection with the instantaneous rotation of a test object inserted at any point in the field. But it does not inform about the space, just the vector field.

Hi rpenner.

What if the "abstract vector field" is mathematically modeling a 'real energy-space field'?

I ask this because some mathematician-physicists have claimed that the math models the reality.

Now you are saying that "it's just abstract math applied to an abstract vector field".

So the question indicated is: Which is it....is the math treating real physical energy-space field or not? If yes, then Farsight is justified in treating 'curl' as a real physical phenomena/property of energy-space field. If no, then mathematics cannot be used as a basis for arguing against the validity of Farsight's treatment either way.


Just impartial observation on the implications of the above-quoted. No claims are intended to be made or dismissed hereby.

Cheers!

.

 

[przyk]

Sorry pryzk, I can't show you some root-and-branch development of electromagnetism. But I'll have a dig around for something by somebody that numerically predict any of the usual, routine predictions of electromagnetism.

This should be your first priority, not an afterthought.

 

[AlphaNumeric]

For example E tells you how a dynamical frame-dragging roton moves linearly with respect to another rather being a some magic field that makes some static point-particle thing move in a mysterious way. It's like, you take curl at face value, space is curved in more than one dimension, this diminishes with distance, and it isn't like that for nothing. Play with paper strips, gyroscopes, Falaco solitons, hairballs, and look at gravitomagnetism. Then you'll see it.

I am absolutely certain that if I'd made a post like that but with the first few words being "String theory says...." you'd have utterly dismissed it for making no viable predictions, having no justification, no demonstrably relevance to the real world.

I asked you a direct question in my last post....

Why don't you hold your own claims to standards you attempt to hold the mainstream to? Why is it okay for you to have absolutely nothing of any substance, especially quantitative testable models, yet you complain string theory has nothing like that (which is false)?

This isn't a rhetorical question Farsight.

Seeing as you ignored it, and not for the first time, I'll take it to mean you cannot answer it without admitting considerable hypocrisy on your part.

Noted RJ. I did mean to be sincere, and if I come over as condescending I can only apologise and resolve to check what I post before I hit the ENTER key.

As my last post said, your posts give the distinct impression you view yourself as a knowledgeable teacher passing nuggets of 'the truth' down to us lesser mortals who made the 'mistake' of learning the mainstream's take on things. Given your complete inability to justify your claims, answer direct questions or admit to hypocrisy such an attitude is arrogant and worse, unduly arrogant. If you could demonstrate you had some reason for your attitude, something from all of your claims actually is physically viable, then that'd at least be something. Instead this constant "Think about it. You'll see it!" nonsense is just ridiculous.

So ask yourself, what is this field?

Whether or not Rpenner or anyone else has an answer you have not given any reason for anyone to think you know the answer.

Ordinarily people say "ah, that's because of the electromagnetic field", but they don't actually ask themselves what this thing is.

Your choice of wording is very telling. 'Ordinary people'? Since you do ask yourself that question you must therefore believe yourself extraordinary.

This is good stuff. Yes, it's written for the layman,

Such as yourself.

Make the connection.

You keep telling people to make connections but you haven't made the connection that all of your 'interpretations' are disputable, if not actually refuted, and that your approach isn't getting you anywhere. Make the connection.

If this thread continues much more than either myself or Prom will end up ripping out all the Farsight related stuff and shifting it to pseudoscience. I offered Farsight the chance to explain why he isn't doing pseudoscience and he's not even been honest enough to say "I can't", he's just ignored me.

 

[przyk]

But when Einstein said space, he was talking about space space.

If Einstein was just talking about space, why is all of general relativity 3+1 dimensional Riemannian geometry? Why is the geodesic equation given in 3+1 dimensions? As I pointed out in a [POST=2727436]previous post[/POST], not only is it obvious that Einstein was working in 4 dimensional spacetime throughout his original paper on GR, but this is necessary in order for GR to be able to recover Newtonian gravity.

To anyone who's ever learned GR in any detail (read: well enough to understand how predictions are calculated from it), there's just no ambiguity about this.

However there's no motion through spacetime.

Why do you keep repeating this mantra as if it were supposed to mean something? We've been over this before and it seems to make no impact no matter how often it's explained to you: motion, even in "spacetime", means the exact same thing it always did.

Seriously, if the world's ultra number one super fan of "spacetime", with Minkowski diagrams on his t-shirt and cap and a matching thermos flask, told you "I moved my car out of the garage this morning", would you really have trouble understanding what they meant by that?

 

[Farsight]

If Einstein was just talking about space, why is all of general relativity 3+1 dimensional Riemannian geometry? Why is the geodesic equation given in 3+1 dimensions?

Because when light moves through a region of space where we say a gravitational field is present, it curves.

As I pointed out in a [POST=2727436]previous post[/POST], not only is it obvious that Einstein was working in 4 dimensional spacetime throughout his original paper on GR, but this is necessary in order for GR to be able to recover Newtonian gravity. To anyone who's ever learned GR in any detail (read: well enough to understand how predictions are calculated from it), there's just no ambiguity about this.

But there does seem to be an issue with curved spacetime.

Why do you keep repeating this mantra as if it were supposed to mean something? We've been over this before and it seems to make no impact no matter how often it's explained to you: motion, even in "spacetime", means the exact same thing it always did.

Because prometheus asked about it, and it's important.

Seriously, if the world's ultra number one super fan of "spacetime", with Minkowski diagrams on his t-shirt and cap and a matching thermos flask, told you "I moved my car out of the garage this morning", would you really have trouble understanding what they meant by that?

No. But if he said I threw a ball across my garage and it arced towards the ground because the spacetime it's moving through is curved, I'd point out that Minkowski spacetime is an all-times mathematical space. And as such, there can be no motion through it, so he's confusing cause and effect. Then I'd point to Einstein talking about inhomogeneous space and the state of space, and saying a curvature of rays of light can only take place when the velocity of propagation of light varies with position. If he replied saying velocity is a vector quantity and the light changes direction, I'd show him the original German, which says die Ausbreitungs-geschwindigkeit des Lichtes mit dem Orte variiert, and translates to the speed of light varies with the locality. Then I'd show him two parallel-mirror light clocks at different elevations which lose synchronisation, and thus where it's plain to see that this is happening:

|--------------|
|--------------|

Then maybe we'd get talking about the state of space and things like Z[sub]0[/sub] = √(μ[sub]0[/sub]/ε[sub]0[/sub]) and c = √(1/ε[sub]0[/sub]μ[sub]0[/sub]).

 

[Farsight]

I am absolutely certain that if I'd made a post like that but with the first few words being "String theory says...." you'd have utterly dismissed it for making no viable predictions, having no justification, no demonstrably relevance to the real world.

If you offered a coherent explanation illuminated with analogies and which referred back to Minkowski and Maxwell saying things like...

"Then in the description of the field produced by the electron we see that the separation of the field into electric and magnetic force is a relative one with regard to the underlying time axis; the most perspicious way of describing the two forces together is on a certain analogy with the wrench in mechanics, though the analogy is not complete".

"A motion of translation along an axis cannot produce a rotation about that axis unless it meets with some special mechanism, like that of a screw."

...I wouldn't dismiss it, I'd be really interested.

I asked you a direct question in my last post....

Seeing as you ignored it, and not for the first time, I'll take it to mean you cannot answer it without admitting considerable hypocrisy on your part.

I ignore you because you're dishonest, and it just isn't possible to have a sensible conversation with you. For example, let's look at that question:

Why don't you hold your own claims to standards you attempt to hold the mainstream to? Why is it okay for you to have absolutely nothing of any substance...

There. I refer to Einstein, Minkowski, Maxwell, and others, plus experimental evidence, and you attempt to assert that I have absolutely nothing of any substance.

...especially quantitative testable models, yet you complain string theory has nothing like that (which is false)? This isn't a rhetorical question Farsight.

It's a discussion forum. I complain that string theory has no evidential support. I've said before that if a new theory lacks experimental support we cut it some slack. But if it's been going for decades, and there's still no supporting evidence, in the end we have to look elsewhere.

As my last post said, your posts give the distinct impression you view yourself as a knowledgeable teacher passing nuggets of 'the truth' down to us lesser mortals who made the 'mistake' of learning the mainstream's take on things.

Sorry about that.

Given your complete inability to justify your claims, answer direct questions or admit to hypocrisy such an attitude is arrogant and worse, unduly arrogant. If you could demonstrate you had some reason for your attitude, something from all of your claims actually is physically viable, then that'd at least be something. Instead this constant "Think about it. You'll see it!" nonsense is just ridiculous.

I'm giving justification and answering questions.

Whether or not Rpenner or anyone else has an answer you have not given any reason for anyone to think you know the answer.

If somebody asks a question, I'll try to give an answer.

Your choice of wording is very telling. 'Ordinary people'? Since you do ask yourself that question you must therefore believe yourself extraordinary. Such as yourself.

I said Ordinarily.

You keep telling people to make connections but you haven't made the connection that all of your 'interpretations' are disputable, if not actually refuted, and that your approach isn't getting you anywhere. Make the connection.

I'm quite pleased with how things are moving actually. We'll get there.

If this thread continues much more than either myself or Prom will end up ripping out all the Farsight related stuff and shifting it to pseudoscience. I offered Farsight the chance to explain why he isn't doing pseudoscience and he's not even been honest enough to say "I can't", he's just ignored me.

I ignore you because you make spurious ad-hominem accusations instead of entering into the discussion with sincerity.

 

[RJBeery]

Why do you keep repeating this mantra as if it were supposed to mean something? We've been over this before and it seems to make no impact no matter how often it's explained to you: motion, even in "spacetime", means the exact same thing it always did.

Seriously, if the world's ultra number one super fan of "spacetime", with Minkowski diagrams on his t-shirt and cap and a matching thermos flask, told you "I moved my car out of the garage this morning", would you really have trouble understanding what they meant by that?

I think Farsight is just trying to point out two concepts that some people don't take care to differentiate. Motion through space is modeled as 3+1 spacetime; motion through spacetime is not possible. Spacetime, as a whole, is essentially BLOCK TIME (hence my affinity for this particular message of his).

 

[Farsight]

That's the crucial point, RJ. When you search on because spacetime is curved you come to appreciate that a lot of people don't make a distinction between space and spacetime. They think light bends because space is somehow curved, and they don't pay attention to what Einstein actually said about the state of space. It's something to do with the "paradigm shifts" of the Golden age of general relativity I suppose, epitomised by "Matter tells space how to curve. Space tells matter how to move" which I think is pretty dire myself. An interesting thing to read is Einstein's The History of Field Theory dating from 1929, where you can see things like this:

...The first body brings the space immediately around it into a certain condition which spreads itself into more distant parts of space, according to a certain spatio-temporal law of propagation. This condition of space was called "the electric field."

...But the special theory of relativity showed that this causal correlation corresponds to an essential identity of the two types of field. In fact, the same condition of space, which in one coordinate system appears as a pure magnetic field, appears simultaneously in another coordinate system in relative motion as an electric field, and vice versa.

...By making use of empirically known properties of space, especially the law of the propagation of light; it is possible to show that the space - time continuum has a Riemannian metric.

...It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds, and it is natural to suspect that this only appears to be so because the structure of the physical continuum is not completely described by the Riemannian metric.

 

[przyk]

Because when light moves through a region of space where we say a gravitational field is present, it curves.

That doesn't answer my question: why Riemannian geometry, and why 3+1 dimensions?

But there does seem to be an issue with curved spacetime.

What issue?

Because prometheus asked about it, and it's important.

Where did prometheus use the phrase "motion through spacetime" in this thread?

No. But if he said I threw a ball across my garage and it arced towards the ground because the spacetime it's moving through is curved, I'd point out that Minkowski spacetime is an all-times mathematical space. And as such, there can be no motion through it, so he's confusing cause and effect.

No. You could define the word "motion" in such a way that the phrase "motion through spacetime" was technically meaningless. Or you could allow the word "motion" to be used in a more flexible manner such that the phrase "motion through spacetime" becomes technically acceptable. Either way this is just a silly argument over terminology, made even sillier by the fact that prometheus didn't even use it in this thread.

If he replied saying velocity is a vector quantity and the light changes direction, I'd show him the original German, which says die Ausbreitungs-geschwindigkeit des Lichtes mit dem Orte variiert, and translates to the speed of light varies with the locality.

Specifically, what we'd now call the coordinate speed of light can vary with position.

 

[przyk]

I think Farsight is just trying to point out two concepts that some people don't take care to differentiate.

Funny, I had the opposite impression: people start off thinking there's some physical difference between "space and time" and "spacetime" until they really think about it and realise they can't define any meaningful distinction. They're different notations, not different theories.

Motion through space is modeled as 3+1 spacetime;

I'm not sure what you mean. The 3+1 is a reference to the metric signature in relativity.

motion through spacetime is not possible.

That depends on how strict you want to be with the word "motion" more than anything else.

Spacetime, as a whole, is essentially BLOCK TIME (hence my affinity for this particular message of his).

Try defining the phrase "block time". Can you think of an experiment we could perform that could distinguish "block time" from "non-block time", or whatever you want to call it? Because otherwise I don't see any meaningful difference.