Relativity (split from Can relativity be applied to light speed?)

[Ghideon]

5 hours ago, studiot said:

have three points nobody seems to have considered, to add to this discussion.

Good points!

I was only considering what, AFIK, is possible in our universe.

Question about first one; would multiple objects, separated by enough space to be causally not connected, be the same situation mathematically? I mean, before the objects would have had a chance to affect each other, would the same math apply to each object? The object could be one of several in the universe but must be alone in its own observable region of the universe. (Example: gravitational waves propagating at light speed.) 

 

Note: I'm not stating that you comment is incorrect, just that I got curious about how this works in the context of the original question stated.

[Mordred]

If particles A and B have no shared causality then the two cannot affect each other.

[studiot]

1 hour ago, Ghideon said:

Good points!

I was only considering what, AFIK, is possible in our universe.

Question about first one; would multiple objects, separated by enough space to be causally not connected, be the same situation mathematically? I mean, before the objects would have had a chance to affect each other, would the same math apply to each object? The object could be one of several in the universe but must be alone in its own observable region of the universe. (Example: gravitational waves propagating at light speed.) 

 

Note: I'm not stating that you comment is incorrect, just that I got curious about how this works in the context of the original question stated.

 

Well the original question says that the body never experiences a force. But it does not say for how long this period of grace last in the history of the body.

I also mentioned momentary conjunctions of the generators of forces acting on the body where the net force is zero.

 

Obviously, in a universe where nothing is moving, no matter how far apart (in space) two bodies are, the 'force field' generated by one will eventually affect the other, though there will be a time lag.

The bodies may however be moving so that causal connection comes into play, as Mordred comments.
But I would add a rider to his comment that causal connection is not immune from disturbance by a third body which may push something into or out of the connection light cone region.

 

[Strange]

2 hours ago, studiot said:

Well the original question says that the body never experiences a force. But it does not say for how long this period of grace last in the history of the body.

Never means never! (As some British PM nearly said.)

[MPMin]

20 hours ago, Strange said:

You would be saying that you, for example, are moving at an infinite number of different speeds in an infinite number of different directions. All at the same time. How is that useful?

 So I have no idea what you are suggesting or why.

Because it seems inaccurate to only pick the nearest or most relevant frame of reference when in fact your frame of reference is also moving in relation to another frame of reference and so on.

20 hours ago, Strange said:

20 hours ago, MPMin said:

Exactly! And at some point science has to just take a guess and say it just appeared there out of now where like magic.

No it doesn't. And never does.

A hypothesis is basically a guess. If you want to get into an argument about this consider who’s the educated one; the guess or the person making the guess...

[Strange]

17 minutes ago, MPMin said:

Because it seems inaccurate to only pick the nearest or most relevant frame of reference when in fact your frame of reference is also moving in relation to another frame of reference and so on.

I’m not sure you know what a frame of reference is. 

How can it be “more accurate” to say you are moving at an infinite number of different speeds in an infinite number of different directions at the same time?

[MPMin]

1 hour ago, Strange said:

2 hours ago, MPMin said:

Because it seems inaccurate to only pick the nearest or most relevant frame of reference when in fact your frame of reference is also moving in relation to another frame of reference and so on.

I’m not sure you know what a frame of reference is. 

 How can it be “more accurate” to say you are moving at an infinite number of different speeds in an infinite number of different directions at the same time?

Like this:

 

22 hours ago, swansont said:

22 hours ago, MPMin said:

There is such a frame of reference it’s just impractical to use 

Quite the opposite. The center-of-momentum frame is often extremely useful. Or the center-of-mass. Or one object being at rest. The thing is that the physics works just as well in any other inertial frame. There is nothing special about any inertial frame, from a physics perspective. You can use whichever one makes the problem easiest to solve.

 In any given problem, you may not know the history, so you can't tell if there had been a force applied to the object. 

I’m suggesting picking a point that’s considered the centre of the universe as the frame of reference 

[Bufofrog]

56 minutes ago, MPMin said:

I'm suggesting picking a point that’s considered the centre of the universe as the frame of reference 

Why?  What do you think that would accomplish?

[studiot]

1 hour ago, MPMin said:

I’m suggesting picking a point that’s considered the centre of the universe as the frame of reference 

A point is not a frame (hint that is why we have separate words).

Besides which the Universe as a whole has no centre.
Swansont's reference to a centre was referring to a finite system of bodies not the whole universe.

[Strange]

1 hour ago, MPMin said:

Like this:

 

I’m suggesting picking a point that’s considered the centre of the universe as the frame of reference 

There is no centre of the universe.

However, we are at the centre of the observable universe, so an Earth centred frame of reference is used for a lot of applications.

And, on cosmological scales, the comoving coordinates are used.

Thery are perhaps the nearest thing to what you suggest. But you wouldn't use either of those to navigate to your friend's house.

[swansont]

2 hours ago, MPMin said:

Like this:

 

I’m suggesting picking a point that’s considered the centre of the universe as the frame of reference 

1. There is no center

2. Picking a point is a choice, rather than having it dictated by physics. 

[MPMin]

43 minutes ago, Strange said:

There is no centre of the universe.

However, we are at the centre of the observable universe, so an Earth centred frame of reference is used for a lot of applications.

And, on cosmological scales, the comoving coordinates are used.

 Thery are perhaps the nearest thing to what you suggest. But you wouldn't use either of those to navigate to your friend's house.

You’re right, (except my friend could be ET) but this brings me back to the momentum query; with reference to the entire observable universe, assuming the Big Bang occurred out of nowhere we should be able to assume the universe as a whole has no momentum, its expanding but its centre-of-momentum is zero, with this frame of reference we can more accurately (and by accurately I mean consistently) determine the momentum of celestial objects.

The universe has no centre - that we know of as we don’t even know if it is infinite or finite 

Yes I’m suggesting choosing a point to call the centre of the universe, if we can have a tentative beginning to the universe lets give it a tentative centre as well.

[studiot]

7 minutes ago, MPMin said:

its expanding but its centre-of-momentum is zero, with this frame of reference we can more accurately (and by accurately I mean consistently) determine the momentum of celestial objects.

 

Enough pseudomathematics.

"more accurately" is a mathematical statement but I see no mathematics.

Furthermore the rules here require answers to polite questions and comments from other members

 

Edited August 17, 2019 by studiot

[Strange]

You can choose any point you like as the centre of the universe. It really doesn't matter.

But you would probably better of choosing a point that is useful for the measurements you need to do. 

[MPMin]

59 minutes ago, studiot said:

Furthermore the rules here require answers to polite questions and comments from other members

 

I felt that my response addressed your question as well, I wasn’t ignoring you I just didn’t quote you as well.

I just don’t understand how an object’s momentum can change by simply changing the frame of reference. 

For example, if you were to simultaneously fire two bullets side by side at the same target, the bullets while travelling to the target have almost no moment relative to each other but relative to the target they do. I just cant see the point of ignoring forces the bullets experienced while being fired. The bullets poses kinetic energy from the gun powder explosion and that kinetic energy still exists in those bullets wether you take the point of view from one of the bullets or not. I know that in this example you wouldn’t practically have time to only consider the bullets relative to each other but in much larger objects travelling far greater lengths of time the same principle should apply by choosing a fixed frame of reference.

 

[Janus]

49 minutes ago, MPMin said:

I felt that my response addressed your question as well, I wasn’t ignoring you I just didn’t quote you as well.

I just don’t understand how an object’s momentum can change by simply changing the frame of reference. 

For example, if you were to simultaneously fire two bullets side by side at the same target, the bullets while travelling to the target have almost no moment relative to each other but relative to the target they do. I just cant see the point of ignoring forces the bullets experienced while being fired. The bullets poses kinetic energy from the gun powder explosion and that kinetic energy still exists in those bullets wether you take the point of view from one of the bullets or not. I know that in this example you wouldn’t practically have time to only consider the bullets relative to each other but in much larger objects travelling far greater lengths of time the same principle should apply by choosing a fixed frame of reference.

 

For a reference frame with a relative velocity with respect to the guns equal to that which the bullets have relative to the gun after being fired,  the bullets start with a non-zero kinetic energy and momentum due to the velocity they have relative to the above reference frame before the guns are fired.   The guns firing produces forces that, as seen from this frame act as a "brake" on the bullets, slowing their velocity to zero, and lowering their relative KE and momentum to zero.

From the bullet's point of view, they were making measurements from one inertial frame before firing, and a different one after.  They spent a brief period in an accelerated non-inertial frame.   So while they can infer that they changed momentum and KE in the transition between the two inertial frames, all they can really say is that the KE and Momentum is different after firing than before firing.  They cannot say anything about their absolute KE or momentum.

[MigL]

The Big Bang didn't originate at a 'center' or any specific location.
It originated EVERYWHERE.
( once you come to grips with this, you understand more cosmology than 99 % of the population )

Further, properties like momentum, energy, velocity, etc. are all frame dependant; and anytime you specify one of these quantities, you need to specify "relative to what". ( that's where the term Relativity comes from )
As you seem to have difficulty with the definition of a FoR, I suggest a google search for some clarification.

That being said, the closest thing to a 'universal' reference frame ( I stress, no such thing exists ), is the CMB. This is the left-over glow from when matter in the universe consisted of opaque, decoupled plasma, approximately 300 mil yrs after the Big Bang event. I cannot say the 'observable' universe, as that has changed over the past 13.4 bil yrs. Our galaxy's direction of motion, and speed, relative to this 2.7 deg 'glow', can be calculated from the amount of 'blue' shift ( of the CMB glow ) in the direction of travel.
But you must understand that this is NOT a real 'universal' frame.
( that is impossible for mathematical reasons )

[swansont]

On 8/17/2019 at 8:51 AM, MPMin said:

Yes I’m suggesting choosing a point to call the centre of the universe, if we can have a tentative beginning to the universe lets give it a tentative centre as well.

You can pick any inertial frame you want. It doesn’t matter. The physics is the same in all of them.

On 8/17/2019 at 10:00 AM, MPMin said:

I just don’t understand how an object’s momentum can change by simply changing the frame of reference. 

It doesn’t change, as such. It’s different. In one frame it’s at rest and has no momentum. In any other it’s moving, and p = mv

 

[MigL]

Sorry, I keep mis-typing the number...
The relic radiation of the CMB is from approx. 300 thou yrs after the BB event.
( could not edit previous post )

[MPMin]

On 8/19/2019 at 7:43 AM, MigL said:

The Big Bang didn't originate at a 'center' or any specific location.
It originated EVERYWHERE.
( once you come to grips with this, you understand more cosmology than 99 % of the population )

I am at grips with this (theory), I was just curious about defining momentum in absolute terms. 

[Strange]

17 hours ago, MPMin said:

I was just curious about defining momentum in absolute terms. 

You can’t. Not just theoretically, Lorentz invariance has been tested to incredible levels of accuracy

[Schmelzer]

On 8/16/2019 at 5:59 PM, Strange said:

No, there isn't. (Well, there is. The trouble is there are an infinite number of them.)

But among that infinite number it is quite easy to make a choice.  If one  assumed that some theory beyond GR, say QG, will define an absolute space, one would have to specify equations which distinguish absolute space, thus, a condition which would distinguish the preferred coordinates. But there is essentially only one candidate for such a condition, namely harmonic coordinates.

And there is also a single distinguished set of such particular harmonic coordinates, namely the comoving coordinates of the FLRW ansatz.  For zero spatial curvature, which is what we observe, the FLRW ansatz would be [math]ds^2 = d\tau^2 - a^2(\tau)(dx^2+dy^2+dz^2)[/math], and the coordinates x,y,z are harmonic.

Absolute time would have to be harmonic too, but this is also not difficult, the slightly modified ansatz [math]ds^2 = a^6(t)dt^2 - a^2(t)(dx^2+dy^2+dz^2)[/math] has already a harmonic time coordinate too, so that harmonic time and proper time are connected by the simple equation [math] d\tau = a^3(t)dt.[/math] 

This would be the only choice where the Copernican principle holds, with no center of the universe.  So, to make a plausible choice among that infinite number is very easy, no trouble at all.

[studiot]

 

39 minutes ago, Schmelzer said:

On 8/16/2019 at 12:29 PM, Strange said:

No, there isn't. (Well, there is. The trouble is there are an infinite number of them.)

But among that infinite number it is quite easy to make a choice.  If one  assumed that some theory beyond GR, say QG, will define an absolute space, one would have to specify equations which distinguish absolute space, thus, a condition which would distinguish the preferred coordinates. But there is essentially only one candidate for such a condition, namely harmonic coordinates.

And there is also a single distinguished set of such particular harmonic coordinates, namely the comoving coordinates of the FLRW ansatz.  For zero spatial curvature, which is what we observe, the FLRW ansatz would be ds2=dτ2−a2(τ)(dx2+dy2+dz2) , and the coordinates x,y,z are harmonic.

Absolute time would have to be harmonic too, but this is also not difficult, the slightly modified ansatz ds2=a6(t)dt2−a2(t)(dx2+dy2+dz2) has already a harmonic time coordinate too, so that harmonic time and proper time are connected by the simple equation dτ=a3(t)dt.  

This would be the only choice where the Copernican principle holds, with no center of the universe.  So, to make a plausible choice among that infinite number is very easy, no trouble at all.

A word of caution here.

The OP of this thread based his disscussion of 3-Momentum which is frame (observer) dependent.
And that will have been the background to Strange's comment.

Your equations pertain to 4-Momentum which is quite a different animal, used and understood by many of the other participants in this thread.