Constancy of SOL from all objects

[Mordred]

Sooooo...

 

All observations/measurements are valid/real in the frame they're made in.

 

 

this is the key point behind the statement. "there is no preferred frame of reference"

 

When you think about it the purpose of relativity is to explain why different observers measure the same event differently.

 

Lets use some basic math to illustrate.

 

Measured frequency of Cows color.

 

Observer a.

 

emitted color frequency= color percieved

 

observer b

 

emitted color frequency+ redshift =color percieved.

 

 

mathematically formula one is identical to formula two its just redshift =0 for observer a.

 

Both are equally accurate measurements because the RHS specifies color percieved.

They both agree that different redshifts will change the color percieved.

 

This is the same on redshift. All observers need to use the same emitter frequency (which is your measured event) but have different reference frames which is the observer events.

 

As each observer is effectively a different distance and has a slightly different time within his own reference frame. They get different results. Does this mean they are wrong?

 

 

no because they are following the same formula. If they subtract the observer redshift variation from the above equations. They will both conclude the same emitter frequency.

 

Lets look at an official formula you had trouble with on another thread.

 

[latex]v_{recession}=H_oD [/latex].

 

the galaxies velocity not apparent velocity is dictated by Newtons laws and the conservation of energy/momentum. This part has nothing to do with observers and the above equation.

 

The observers using the above equation are not trying to describe the galaxies momentum due to conservation of momentum and Newtons laws.

 

They are measuring the observer offset due to location and expansion. (personally we would be better off calling recessive velocity, Hubble recession). but were stuck with an inaccurate and misleading terminology for historical reasons.

 

recessive velocity has nothing to do with the laws of inertia or conservation of momentum. Its just an observer offset due to location of the observer. As it doesnt involve the laws of inertia or conservation laws its not a velocity but an apparent or peculiar velocity. (even worse its measuring the change in a commoving volume. The formula above desribes its past location. not its distance today. Commoving vs proper distance) but thats another complexity for another thread....

 

Lets create a more flexible formula.

 

emitter =A

observer variation =B

observer measurement=C.

 

[latex]A+B=C [/latex]

 

So you have numerous observers who measure a. Each has his own observer variation B. So each will arrive at a different value for C.

 

Every observer is equally correct accordingly to the above formula for value C at his location. If each observer subtracts B from C they will calculate (not measure ) the same value for A.

 

As long as all observers can calculate the same value for A using the same observer variation metrics in B. We know A is the closest representation to reality. What each observer calculates to be the same after they subtract the observer variation B from Observer measurement C.

 

(no observer will truly have observer variation B=0. There is always some location or gravitational potential offset regardless of how miniscule).

 

But that doesnt matter as long as all observers can calculate the same value for A.

 

Hint B can be any metric provided all observers agree on that metric. (invariant metric).

 

Hint 2 There is no preferred frame as we cannot define any observer reference frame where we can accurately state Observer variation =0. Its nearly impossible to have both events in precisely the same reference frame. (at best its to good approximation)

 

 

[latex]\colorbox{red}{You have been thinking C equals reality.}[/latex]

 

[latex]\colorbox{red}{But measurements done by an observer never precisely measures reality.}[/latex]

Edited July 31, 2016 by Mordred

[swansont]

Is that the only point that bothers you in my post?

Beyond that, I don't really care.

[michel123456]

[latex]\colorbox{red}{You have been thinking C equals reality.}[/latex]

 

[latex]\colorbox{red}{But measurements done by an observer never precisely measures reality.}[/latex]

if C is a frame, it is the best available.

And the more you get away from C, the more it gets elusive (bis repetita placent).

[Mordred]

The more you get away from A not C. A is your closest to reality. A is the source being measured. B is any variation (regardless of cause) between the Source A to measured value.

Edited July 31, 2016 by Mordred

[swansont]

if C is a frame, it is the best available.

And the more you get away from C, the more it gets elusive (bis repetita placent).

 

 

Is there any way to show that this is true?

[Markus Hanke]

This frame measures proper length (1), proper time(2), proper mass (3 rest mass) in as much as possible present time(4).

 

 

That would be the rest frame of the object, which is a perfectly valid frame of reference. But then again, so is every other frame of reference, because they are all subject to the exact same laws of physics. This is one of the crucial points here - all inertial observers experience the same laws of physics, therefore no one frame can be taken as "preferred" or "privileged"; they are all equally valid. And that can be proven mathematically.

 

To briefly come back to the donut example - the donut, in spacetime, would look somewhat like two nested tubes with an internal structure ( since one dimension is suppressed for reasons visualisability of course ). You get the point of view of a specific observer simply by intersecting that "world tube" by a plane that is inclined with respect to the coordinate axis - different angles correspond to different observers, so going from one observer to another means you change the inclination angle of your intersecting plane, thereby trading space for time and vice versa, and hence you get a different cross section. That is why observers moving at different speeds relative to some reference point see the donut in different ways ( more generally - they see a different "mix" of space and time ), even though they are always considering a projection of the same 4-dimensional structure. The only difference between them is an angle - and that's why you can express the motion ( speed ) of inertial observers as a simple angle in spacetime - this angle is called "rapidity". It's just simple geometry.

 

 

 

There are no 300 overlapping realities*, and putting measurements above that is madness.

 

Yes, you are exactly correct - there is only one reality, and that is the reality of events in 4D spacetime. You can define measurements of space and time ( i.e. projections of the 4D reality into 3D space ), but these constitute only limited perspectives, and are thus not something that all observers can agree on. Nonetheless, even though different ways to project the same thing into 3D may look superficially different, they are all still equally valid projections which are related in quantifiable and well defined ways. They are all equally valid aspects of reality, and hence "real" in their own right, but none of them conveys the whole picture. For that, you need to look at the situation in 4D.

 

Once everything is said and done, what remains is the scientific method. In physics, we are trying to make models that describe the world around us, so the question essentially becomes whether the model is a good one, in the sense that the predictions we extract from it correspond with the available empirical data. The 4D spacetime model ( i.e. relativity ) does exceedingly well in that regard, not just in the classical world, but also in the microscopic realm - local Lorentz symmetry of SR implies CPT symmetry in quantum field theory, so it also underlies almost all of what we know about the behaviour and interactions of elementary particles. Furthermore, it dictates some innate properties of those particles themselves - for example, the property of spin can be taken as an essentially relativistic phenomenon, it arises from the way the descriptions of particles behave under transformations in spacetime. And so on.

 

Basically, what I am attempting to point out is that the 4D spacetime point of view isn't ad-hoc and arbitrary, but there are very good reasons for adopting that perspective, since it reveals physics that are not apparent in the old Newtonian description.

Just to make this perfectly explicit again. Consider a tin can, and how it appears from different perspectives :

 

 

One observer sees the tin can be a circle, the other one sees it to be a rectangle; they could not possibly disagree more. But nonetheless, there is only one reality - the tin can itself. There is no problem, no issue to be resolved, no inconsistency, no paradox. The confusion arises only when one insists that the shadows on the wall must be the object itself, to the exclusion of the bigger picture in 3D. But once one goes beyond the seemingly conflicting 2D projections and adopts the 3D point of view instead, then all disagreements are immediately exposed to be only apparent.

 

The same is true in relativity - observers disagree on measurements of space and time in different frames, but once they adopt the 4D spacetime point of view, it becomes clear that these disagreements are merely apparent, because they are only projection of the one reality, just like for the tin can above. Relativity is not the source of contradictions and problems - it is the solution to it. Before relativity, confusion reigned supreme, because there appeared to be conflicting formulations of physical laws that couldn't be reconciled - it took a paradigm shift away from 3D space + time towards spacetime, and all apparent paradoxes immediately disappeared.

Edited August 1, 2016 by Markus Hanke

[Strange]

Just to make this perfectly explicit again. Consider a tin can, and how it appears from different perspectives :

 

 

 

One observer sees the tin can be a circle, the other one sees it to be a rectangle; they could not possibly disagree more.

 

 

And, just to make this absolutely clear to Michel, this disagreement is not resolved by arbitrarily choosing one of these views as "best". Which is what he is doing.

 

It is resolved by looking at the "big picture" - the 3D object considered from all directions simultaneously.

 

That is what GR does: it says that the "proper" measurements (those made in the object's own rest frame) are just as much an "illusion" or distortion as any other. The only "true" view is the invariant one that considers relationships between events in space-time

[Delta1212]

 

 

And, just to make this absolutely clear to Michel, this disagreement is not resolved by arbitrarily choosing one of these views as "best". Which is what he is doing.

 

It is resolved by looking at the "big picture" - the 3D object considered from all directions simultaneously.

 

That is what GR does: it says that the "proper" measurements (those made in the object's own rest frame) are just as much an "illusion" or distortion as any other. The only "true" view is the invariant one that considers relationships between events in space-time

Further clarifying: The rest frame measurement is not "the can." It is just one more shadow among many. It's the shadow we're most used to dealing with and have the most intuitive understanding of, but that is still not the same as actually being the can, or even being the most accurate representation of the can.

[michel123456]

 

 

That would be the rest frame of the object, which is a perfectly valid frame of reference. But then again, so is every other frame of reference, because they are all subject to the exact same laws of physics. This is one of the crucial points here - all inertial observers experience the same laws of physics, therefore no one frame can be taken as "preferred" or "privileged"; they are all equally valid. And that can be proven mathematically.

 

To briefly come back to the donut example - the donut, in spacetime, would look somewhat like two nested tubes with an internal structure ( since one dimension is suppressed for reasons visualisability of course ). You get the point of view of a specific observer simply by intersecting that "world tube" by a plane that is inclined with respect to the coordinate axis - different angles correspond to different observers, so going from one observer to another means you change the inclination angle of your intersecting plane, thereby trading space for time and vice versa, and hence you get a different cross section. That is why observers moving at different speeds relative to some reference point see the donut in different ways ( more generally - they see a different "mix" of space and time ), even though they are always considering a projection of the same 4-dimensional structure. The only difference between them is an angle - and that's why you can express the motion ( speed ) of inertial observers as a simple angle in spacetime - this angle is called "rapidity". It's just simple geometry.

 

 

Yes, you are exactly correct - there is only one reality, and that is the reality of events in 4D spacetime. You can define measurements of space and time ( i.e. projections of the 4D reality into 3D space ), but these constitute only limited perspectives, and are thus not something that all observers can agree on. Nonetheless, even though different ways to project the same thing into 3D may look superficially different, they are all still equally valid projections which are related in quantifiable and well defined ways. They are all equally valid aspects of reality, and hence "real" in their own right, but none of them conveys the whole picture. For that, you need to look at the situation in 4D.

 

Once everything is said and done, what remains is the scientific method. In physics, we are trying to make models that describe the world around us, so the question essentially becomes whether the model is a good one, in the sense that the predictions we extract from it correspond with the available empirical data. The 4D spacetime model ( i.e. relativity ) does exceedingly well in that regard, not just in the classical world, but also in the microscopic realm - local Lorentz symmetry of SR implies CPT symmetry in quantum field theory, so it also underlies almost all of what we know about the behaviour and interactions of elementary particles. Furthermore, it dictates some innate properties of those particles themselves - for example, the property of spin can be taken as an essentially relativistic phenomenon, it arises from the way the descriptions of particles behave under transformations in spacetime. And so on.

 

Basically, what I am attempting to point out is that the 4D spacetime point of view isn't ad-hoc and arbitrary, but there are very good reasons for adopting that perspective, since it reveals physics that are not apparent in the old Newtonian description.

Just to make this perfectly explicit again. Consider a tin can, and how it appears from different perspectives :

 

 

One observer sees the tin can be a circle, the other one sees it to be a rectangle; they could not possibly disagree more. But nonetheless, there is only one reality - the tin can itself. There is no problem, no issue to be resolved, no inconsistency, no paradox. The confusion arises only when one insists that the shadows on the wall must be the object itself, to the exclusion of the bigger picture in 3D. But once one goes beyond the seemingly conflicting 2D projections and adopts the 3D point of view instead, then all disagreements are immediately exposed to be only apparent.

 

The same is true in relativity - observers disagree on measurements of space and time in different frames, but once they adopt the 4D spacetime point of view, it becomes clear that these disagreements are merely apparent, because they are only projection of the one reality, just like for the tin can above. Relativity is not the source of contradictions and problems - it is the solution to it. Before relativity, confusion reigned supreme, because there appeared to be conflicting formulations of physical laws that couldn't be reconciled - it took a paradigm shift away from 3D space + time towards spacetime, and all apparent paradoxes immediately disappeared.

Thank you for the long post.

But then, why does it take so long to make people accept that there is only one reality?

Why do scientists insist so much in saying that the oblong rectangle projection or the contracted circular projection are the same "real"? To the point that they believe that they can hold in their hand a can flat as a sheet of paper?

 

 

 

And, just to make this absolutely clear to Michel, this disagreement is not resolved by arbitrarily choosing one of these views as "best". Which is what he is doing.

 

It is resolved by looking at the "big picture" - the 3D object considered from all directions simultaneously.

 

That is what GR does: it says that the "proper" measurements (those made in the object's own rest frame) are just as much an "illusion" or distortion as any other. The only "true" view is the invariant one that considers relationships between events in space-time

This is the weird thing that scientists introduce. Does GR say that? Why do we have to consider what we observe in proper time as "distorted" or as an "illusion".

IMHO what we observe in the same frame as the object is the best frame. Undistorted.

Edited August 2, 2016 by michel123456

[swansont]

 

IMHO what we observe in the same frame as the object is the best frame. Undistorted.

 

 

Can you show this to be true?

[Strange]

Why do we have to consider what we observe in proper time as "distorted" or as an "illusion".

 

Note that I didn't say that what we observer in the objects own frame is distorted (and I put your word "distorted" in quotes).

 

What I said was that it is "just as distorted" as any other frame of reference. They are all equally valid. They are all equally accurate. They are all equally correct. They are none of them distorted. As swansont has repeatedly pointed out, the same laws of physics apply in all frames (which is why we ended up with this model in the first place).

 

 

IMHO what we observe in the same frame as the object is the best frame.

 

That just makes things unnecessarily complicated.