Correlating Newtonian Model with Einstein's GR

[hansda]

I have not read your paper and was responding to the specifics of the comment I quoted. I seldom register/signup in response to an information request, to access any online document.

No need to register or signup. Just click on the link and my paper will appear.

If the question you refer to is embodied by the following from your first post, "See the question (What is the motion of a particle at any instant of time?) in II.6)of my paper.., ",...

Yes. This is the question.

... it seems a vacant question to begin with, since there is no motion of any kind associated with an instant of time.

What do you meant by vacant question? It is a valid question. If no motion of any kind associated with an instant of time, as you opined above; do you think a particle is at rest at any instant of time?

A particle's or object's location may be determined at an instant of time (perhaps not any instant, depending on the information available and inherent limits of certainty). Motion requires a continuous observation of locations over a series of instances.

If a particle is changing locations over a series of instances; that implies a particle has motion at any instant of time.

Still my point re GR remains, that GR is a theory that describes the dynamics of gravitation, not the underlying cause. It is a layman and even to some extent not so lay mistake, to attempt to interpre that Wheeler quote taken out of the greater context. It implies that Spacetime, an inherently 4D mathematical geometry, has some fundamental independent substance... that the geometric description of the dynamics (what we observe), is the cause of what we observe.

If you dont like the term 'curvature of spacetime'; (from the OP) we can say that there is some correlation between IFS/IRF and change of geometry of spacetime, at that instant of time.

 

[OnlyMe]

....

If a particle is changing locations over a series of instances; that implies a particle has motion at any instant of time.

....

If you dont like the term 'curvature of spacetime'; (from the OP) we can say that there is some correlation between IFS/IRF and change of geometry of spacetime, at that instant of time.

hansda,

Motion requires a change in location so no particle or object can be said to have any motion in a single instant of time. When you say an object observed to be in motion, which requires observation over a period of time, can then be implied to be in motion at any instant, the question becomes imaginary or hypothetical... and has no basis in reality. We cannot observe or even record a single instant. BTW I can think of no particle or object anywhere that is at rest, other than relative to a frame of reference which itself connot be at rest, other than relative to itself.

Not to be redundant but, there can be no change in the geometry of Spacetime associated with a single instant of time. Change requires a time period.., that is at least two instances. Which would be unobservable by us, since the process of assembling anything meaningful from what we see, hear etc. requires somewhere in the region of 300 to 400 microseconds (the time it takes our brain to assemble any meaning from what we perceive).... Or an infinite number of instances.

The simple and direct answer is that even for a particle whose location is changing over time, no motion can be attached to the particle for any hypothetical instant of time. Motion requires change and change requires more than a single instant of time.

 

[hansda]

hansda,

Motion requires a change in location so no particle or object can be said to have any motion in a single instant of time. When you say an object observed to be in motion, which requires observation over a period of time, can then be implied to be in motion at any instant, the question becomes imaginary or hypothetical... and has no basis in reality. We cannot observe or even record a single instant. BTW I can think of no particle or object anywhere that is at rest, other than relative to a frame of reference which itself connot be at rest, other than relative to itself.

Not to be redundant but, there can be no change in the geometry of Spacetime associated with a single instant of time. Change requires a time period.., that is at least two instances. Which would be unobservable by us, since the process of assembling anything meaningful from what we see, hear etc. requires somewhere in the region of 300 to 400 microseconds (the time it takes our brain to assemble any meaning from what we perceive).... Or an infinite number of instances.

The simple and direct answer is that even for a particle whose location is changing over time, no motion can be attached to the particle for any hypothetical instant of time. Motion requires change and change requires more than a single instant of time.

Motion of a particle can be either its speed or velocity. Motion can be termed as v(t)=dx/dt. Motion can be considered as a function of time. So, motion of a particle will always have some value at any instant of time. This is the very basics of Physics. https://en.wikipedia.org/wiki/Velocity

 

[OnlyMe]

Motion of a particle can be either its speed or velocity. Motion can be termed as v(t)=dx/dt. Motion can be considered as a function of time. So, motion of a particle will always have some value at any instant of time. This is the very basics of Physics. https://en.wikipedia.org/wiki/Velocity

The first sentence from your above Wiki reference, "The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time."

"Rate of change requires more than a single instant of time.

As I mentioned I have not read your paper, so my comments have been limited to the specific context of your words and wording, as earlier quoted. Initially I thought I was doing no more than pointing out how what you have been saying (perhaps out of context since I have not read your paper) may not be conveying what you intended.

The discussion seems more one of ideology, semantics and perhaps philosophy, rather than physics or even theoretical physics.

As I said earlier, motion requires observation of change over time as indicated by the first sentence Wiki quote above. Even assuming a particle is in motion, "at any instant of time", it is impossible to determine whether it is in motion, inertial or accelerating, or even at rest relative to some arbitrary frame. Any affect the particle's motion may have on anything occurs is a function of a duration of time not any single instant. It is even debatable whether a particle with a charge, like an electron, could have any charge in an instant of time... and the debate could go on and on and on, without any constructive resolution. That frozen instant of time could even be argued to not exist, within the context of any real experience.

I see no point in further discussion of this issue. It seems not just hypothetical, but imaginary.

 

[hansda]

The first sentence from your above Wiki reference, "The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time."

The first sentence also says, velocity is a function of time. That implies motion is also a function of time.

"Rate of change requires more than a single instant of time.

You are correct. That means at every instant of time, it is having some value. Otherwise how you will know the rate of change.

As I mentioned I have not read your paper, so my comments have been limited to the specific context of your words and wording, as earlier quoted. Initially I thought I was doing no more than pointing out how what you have been saying (perhaps out of context since I have not read your paper) may not be conveying what you intended.

The discussion seems more one of ideology, semantics and perhaps philosophy, rather than physics or even theoretical physics.

As you have not read my paper, may be this discussion appears philosophical to you.

As I said earlier, motion requires observation of change over time as indicated by the first sentence Wiki quote above. Even assuming a particle is in motion, "at any instant of time", it is impossible to determine whether it is in motion, inertial or accelerating, or even at rest relative to some arbitrary frame. Any affect the particle's motion may have on anything occurs is a function of a duration of time not any single instant. It is even debatable whether a particle with a charge, like an electron, could have any charge in an instant of time... and the debate could go on and on and on, without any constructive resolution. That frozen instant of time could even be argued to not exist, within the context of any real experience.

Unnecessarily, you are trying to complicate a very simple concept of physics such as "motion".

I see no point in further discussion of this issue.

That is your wish but you could not prove my statement wrong; though you tried hard.

It seems not just hypothetical, but imaginary.

You have not read my paper. Neither you could prove my statement wrong. So you find this discussion hypothetical or imaginary.

Anyway, Thanks for your discussion.

 

[hansda]

I think the question in II.6 of my paper also can be answered in QM. This may help in reconciling QM with Newtonian Model/GR .

 

[hansda]

If the question you refer to is embodied by the following from your first post, "See the question (What is the motion of a particle at any instant of time?) in II.6)of my paper.., ", it seems a vacant question to begin with, since there is no motion of any kind associated with an instant of time.

Is it that, this question can not be answered in GR?

 

[NotEinstein]

I was invited to check this thread by hansda here: http://www.sciforums.com/threads/universe-expansion.159815/page-7#post-3478871 Since I do not see a "correlating NM with GR through [hansda's] TOE", I assume it must be in the PDF linked in the opening post. So let's take a look at it!

The abstract already makes one thing clear: the word "success" here is not used as it is in statistics. Statistics is the closes one would get to a theory of success in mainstream, but when hansda says there are only qualitative and not-mathematical theories in mainstream science, it cannot be referring to that. This reading is confirmed in the first line of the main text, where "success" is described as "a general desire".

The rest of the introduction is introductory, so let's pick it up again at the start of the next section, called "II. Discussion".

'II.1' through 'II.5' introduce our definitions. Note that action is defined significantly different from the mainstream physics usage of the term. Note also the usage of the word "desire". A "doer" thus must possess a mental process, and cannot be lifeless. So for example, a planet cannot be a "doer".

II.6 starts with a pretty okay description of the Newton's first law. The second paragraph seems to be inconsistent with the previous definitions. It uses the phrasing "duration of the action", however, an action is defined as "any movement or motion of a particle with [sic?] relative to an observer". The duration of a motion is ill-defined, as we can always translate into its rest frame. Additionally, does changing a motion "end" the original motion? But this confusion appears to be irrelevant (for now), so let's move on.

The rest of the page just introduces a (non-standard) notation. What is given here is a partial description of standard classical mechanics. Nothing to comment here.
Page 3 (or actually, equation 2) opens with usage of the term "infinitesimal unit of time". It strongly suggests a mis-use of terminology: "two consecutive instants of time" is NOT the proper way to talk about this. However, this may simply be a wording issue, so let's continue.

The last part of II.6 is weird, as a set of forces is being replaced by its sum. However, let's assume this is not signaling an actual correspondence, but just a lingual nicety. Other than that, no comments as this appears to be quite standard classical mechanics, albeit with an unusual notation.

II.7 introduces another definition. Here we encounter a point of interest: a "technique" is coupled to a (single) action, but it is described by its own C(R)FS. However, these are already summed over all forces that affect a particle, so there can be only one. Due to the uniqueness of the C(R)FS, there can only be one technique (per particle) at a time. Thus only one action at a time. This however is consistent with II.6, and we now find our "duration of a motion": it is as long as a certain technique is applied.

II.8 confirms this reading.

II.9 starts with introducing pretty standard mathematical terms. No comment. Then differentation is defined through a combination of a tangent line and infinitesimals. Not sure if this is mathematically sound, but it wouldn't be far off.

Then this: "We know that a point on a straight line is dimensionless ie its radius is zero of has no length." This is non-sensical. We are talking about calculus here, not geometry. Saying a tangent line has zero radius is just mixing different mathematical domains to the point of meaninglessness. Luckily for us, it appears this "radius" has no real impact on the outcome, so we can safely ignore this confused mess.

Page 4 then throws an infinite set our way by "expanding" the real numbers into intervals of size dx, using "infinite" as if it's a number. This is very improper notation, but it's still clear what is meant, so let's see where this leads.

The values of a function are given the same treatment in equation 5. Such a set can either contain a single value multiple times, or we are expected to filter for uniqueness ourselves; that is not made clear.

Then we connect the notation of this set with the CRFS. This is of course problematic, since one set is defined over an infinite interval, the other over a finite (time-)interval. This subtlety is ignored in the text, but infinities are notoriously dangerous to play such tricks with, so I think the equating of these two sets is not sufficiently supported. But... let's say that is was!

CRFS now thus have a function associated with them. Note that this does not necessarily place any restrictions on these functions: they can in principle be discrete, be non-continious, etc.

II.10 contains no new information: it's just putting several definitions together.

II.11 seems to suggest only one technique can lead to a desired result. This may either be sloppy wording, or a property of techniques that I missed. Other than that, nothing spectacular is written here.

II.12 is just a re-statement of things we saw earlier. It however ends with the line "So, this theory also can be considered as a Theory of Everything". What is meant here is that because all actions and techniques are contained within the framework of this theory, it will contain everything. So this is not a theory of everything in the mainstream scientific usage of the word, but a simple statement that the domain of applicability of this theory is the entire universe.

III is supposed to be the conclusion, but it introduces the idea that one can approach success without reaching it. In other words, there is all of a sudden an ordening in outcomes, not just a "single one succes, rest equal". It also says that doers can perform actions by using techniques leading to success. This isn't an insight of any kind; give something the power of choice and this will follow almost necessarily.
This conclusion does however confirm my reading of "Theory of Everything" as I commented on with II.12.

And there the text ends. This is weird, because it appears to be missing its most essential parts! It does not define "success" outside of "doers", thus it places no restrictions on the motions of (for example) fundamental particles or planets. All non-"success" related parts of the text are standard classical mechanics.

I fail to see where any insight might be gained from this text as it currently stands.

And, I also see no derivation of the Einstein field equations, or anything GR related. hansda, you misled me!

 

[DaveC426913]

And what "success" has to do with mechanical physics is still a mystery known only to hansda.
It scores pretty high on the Woo-Salad scale. (a combination of woo-woo and word salad.)

 

[NotEinstein]

And what "success" has to do with mechanical physics is still a mystery known only to hansda.

"Success" is defined by hansda as "an action, by performance of which the doer achieves the desired result. The desired result is as per the choice of the doer". Which clearly signals that some consciousness or mental process has to be present for any "success" to be able to be defined. It indeed is a far cry for anything to do with mechanical physics, and the rest of the text doesn't connect these two dots. There's two parts to this text: the classical mechanics bit, and the "success" bit, but nowhere do they really intersect or connect.

But perhaps hansda can explain it here in this thread. hansda?

 

[The God]

There is a forced connection between the two. If you get into details of GR equations, then the obvious question you can ask is where does 'G' come from in those equations?

It is actually thanks to Newtonian. The claim that limiting case of GR is Newtonian is bad, because both are conceptually different, buy it is used to give legitimacy to flicking 'G' from Newtonian.

 

[NotEinstein]

The claim that limiting case of GR is Newtonian is bad,

Then why can one derive the laws of Newton from GR by taking the limit to weak gravity and low speeds? In other words, why does GR mathematically reduce to Newton when only (relatively) weak gravitational forces are involved and (relatively) small speeds?

 

[QuarkHead]

There is a forced connection between the two. If you get into details of GR equations, then the obvious question you can ask is where does 'G' come from in those equations?

For your education, I write the field equations of gravitation as written down by Einstein........

$$T_{\mu\nu}=R_{\mu\nu}+\frac{1}{2}g_{\mu\nu}R$$ where

$$T_{\mu\nu} $$ are the components of the source tensor
$$R_{\mu\nu}$$ are the components of the curvature tensor
$$R$$ is its trace
$$g_{\mu\nu}$$ are the components of the metric tensor.

Show us where your controversial "G" occurs

 

[The God]

For your education, I write the field equations of gravitation as written down by Einstein........

$$T_{\mu\nu}=R_{\mu\nu}+\frac{1}{2}g_{\mu\nu}R$$ where

$$T_{\mu\nu} $$ are the components of the source tensor
$$R_{\mu\nu}$$ are the components of the curvature tensor
$$R$$ is its trace
$$g_{\mu\nu}$$ are the components of the metric tensor.

Show us where your controversial "G" occurs

Good, so now bring in G? If you do that NotEinstein query will also be covered.

Let me put it differently, if Newtonian gravity was not known beforehand, how would we have introduced G in GR?

 

[NotEinstein]

Good, so now bring in G? If you do that NotEinstein query will also be covered.

The second answer here should save us some tex-layouting time: https://www.quora.com/How-can-we-de...avitation-from-Einsteins-theory-of-relativity

Let me put it differently, if Newtonian gravity was not known beforehand, how would we have introduced G in GR?

It's a constant of nature that pops up, yes, but I don't see how G has to be Newtonian? It was just first introduced by Newton, but it is by no means restricted to Newton's work. Is GR also not "allowed" to use the speed of light, because that's an electromagnetic thing?

 

[The God]

The second answer here should save us some tex-layouting time: https://www.quora.com/How-can-we-de...avitation-from-Einsteins-theory-of-relativity


It's a constant of nature that pops up, yes, but I don't see how G has to be Newtonian? It was just first introduced by Newton, but it is by no means restricted to Newton's work. Is GR also not "allowed" to use the speed of light, because that's an electromagnetic thing?

The link does not say anything about how 'G' gets into the equations.

Yes, I agree with you that Newtonian may not have copyrights over G, but how does this nature's constant pops up in GR?

 

[NotEinstein]

The link does not say anything about how 'G' gets into the equations.

Yes, I agree with you that Newtonian may not have copyrights over G, but how does this nature's constant pops up in GR?

I think it's due to the units of the variables involved. You have to put some constant there, and we call it 'G'.

You could argue that it's not 'G', because there's an $$8\pi$$ there as well. G bar?

Edit: Here's a table with the physical constants (as we know them today):
https://en.wikipedia.org/wiki/Physical_constant#Table_of_physical_constants

'G' is listed under the "Universal constants" section. It's nothing related to Newton specifically; it's related to all things gravitationally.

 

[The God]

I think it's due to the units of the variables involved. You have to put some constant there, and we call it 'G'.

Wish it was so simple.

I like your thinking, very simple indeed.

 

[NotEinstein]

Wish it was so simple.

Why can't it be? This is why "natural units" are a thing: https://en.wikipedia.org/wiki/Natural_units
For historical reasons, the units we tend to use are quite arbitrary, resulting in constants like G in various formulas. But you can simply pick natural units, and G "disappears".

 

[The God]

Why can't it be? This is why "natural units" are a thing: https://en.wikipedia.org/wiki/Natural_units
For historical reasons, the units we tend to use are quite arbitrary, resulting in constants like G in various formulas. But you can simply pick natural units, and G "disappears".

I am not talking about natural units. You have understood that G and 8pi G both have same units, so why only 8 piG why not G or 100000G or why not 0.0000001G? Even this will take you to Newtonian.