# Absolute reference frame

## Main Question or Discussion Point

Hi

I know that the following can never be done in the real world, but in theory, if the vectors of all particles, antiparticles, photons etc. in the universe could be summed, would that qualify as an absolute reference frame for that instant in time?

Clearly each instant would have a different vector sum, but if these sums were traced over a long period of time, it's possible that they would be confined to a sphere somewhere in the universe with a radius that was many orders of magnitude smaller than the universe itself.

Not sure what practical uses such a reference frame would have, but if it is possible, at least theoretically, then it might lead to some interesting ideas.

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The universe does have a preferred frame of reference; you're describing something along the lines of the hubble flow, or being stationary compared to the cosmic microwave background radiation. But the laws of physics seem to behave the same regardless of your relative velocity..

jtbell
Mentor
But the laws of physics seem to behave the same regardless of your relative velocity..
In what sense, then, can one call the CMBR a "preferred reference frame?"

Garth
Gold Member
It is an identifiable reference frame, in the sense that at any location any arbitrary observer, moving at any arbitrary velocity relative to another, can measure the CMB dipole and correct for their peculiar velocity relative to the Surface of Last Scattering. Every observer would then identify the same corrected frame of reference.

Is this result that which is to be expected from the basic principles of GR?

Garth

pervect
Staff Emeritus
Hi

I know that the following can never be done in the real world, but in theory, if the vectors of all particles, antiparticles, photons etc. in the universe could be summed, would that qualify as an absolute reference frame for that instant in time?

Clearly each instant would have a different vector sum, but if these sums were traced over a long period of time, it's possible that they would be confined to a sphere somewhere in the universe with a radius that was many orders of magnitude smaller than the universe itself.

Not sure what practical uses such a reference frame would have, but if it is possible, at least theoretically, then it might lead to some interesting ideas.
While such a frame, if it could be defined, would be interesting, it would not qualify as an absolute frame. An absolute frame is generally understood to imply that no other object is used to construct it. In this case, you are using many objects to construct your frame. So it's just an interesting relative frame.

There is an additional complication. In special relativity, what you describe would work as you think it should, but in general relativity the idea of adding momenta (what you call 'vectors') together to get a 'system momentum' is not well defined in the general case

While there are some important special cases where total momentum can be defined the process is a little more involved than addition. One has to take into account the local metric coefficients as well as the mass and the momenta ('vectors') of the particle.

shouldn't the sum be zero. or else it would be like the universe is moving somewhere.

MathematicalPhysicist
Gold Member
vectors of what, of forces acting on them, of their displacements,of their velocities, of what exactly?

HallsofIvy
Homework Helper
What do you mean by "the vectors" (that's really loop quantum gravity's question). All relevent vectors: force, acceleration, velocity, momentum, are only defined relative to some frame of reference. Starting from a different frame of reference would give different vectors and so a different result for the "sum of all vectors".

Starting from a different frame of reference would give different vectors and so a different result for the "sum of all vectors".
Well here you have it, obviously: magical frame would be where the sum is 0, i.e. all things together do not move anywhere.

jtbell
Mentor
But what would be "magical" about that frame? Suppose we set up a laboratory which is at rest in that (inertial) reference frame, with no windows so we can't "look outside," and nothing from outside can get in. What experiments would work differently inside that laboratory than inside another laboratory which is at rest in a different inertial reference frame (i.e. moving at constant velocity with respect to the first frame)?

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ZapperZ
Staff Emeritus
Well here you have it, obviously: magical frame would be where the sum is 0, i.e. all things together do not move anywhere.
You are making speculative conjecture here.

Ignoring the fact that you haven't answered loop quantum gravity's question, let's try something and then you can tell us where such a thing will apply.

I have a mass at the origin of some coordinate system. At t=0, it explodes into 2 pieces, A and B, going in opposite direction. A and B do not have the same mass, and do not have the same speed.

Now clearly, we know where the "origin" is, and where the "preferred" frame is simply by using the original starting frame. Using this example, can you show us ALL of the so-called vectors that you plan on adding that you conjectured to sum up to zero in this "preferred" frame? Because if you can't show this for this very simple and obvious scenario, what hope can there be for something more complicated like..... oh, I don't know... the universe?

Zz.

A and B do not have the same mass, and do not have the same speed.
Jeez, and what on Earth we will do now? I guess we're screwed, right. Did someone mentioned an impulse? No? Just my imagination then.

ZapperZ
Staff Emeritus
Jeez, and what on Earth we will do now? I guess we're screwed, right. Did someone mentioned an impulse? No? Just my imagination then.
No, I only gave a very simple scenario and asked you to apply on where exactly is this "magical frame" in which the "sum be zero". Are you saying that in this that very simple universe consisting of just 2 end masses, you cannot show such a thing?

Zz.

pervect
Staff Emeritus
Some of the technical points regarding vectors in GR are rather,well, technical. I will give a source that points out that you can't add them together in GR the way you do in SR rather than talk about the details myself. See Baez's

http://math.ucr.edu/home/baez/einstein/node2.html" [Broken]

which also talks a little bit about "relative" vs "absolute" velocities. The following quote is from that URL.

Before stating Einstein's equation, we need a little preparation. We assume the reader is somewhat familiar with special relativity -- otherwise general relativity will be too hard. But there are some big differences between special and general relativity, which can cause immense confusion if neglected.

In special relativity, we cannot talk about absolute velocities, but only relative velocities. For example, we cannot sensibly ask if a particle is at rest, only whether it is at rest relative to another. The reason is that in this theory, velocities are described as vectors in 4-dimensional spacetime. Switching to a different inertial coordinate system can change which way these vectors point relative to our coordinate axes, but not whether two of them point the same way.

In general relativity, we cannot even talk about relative velocities, except for two particles at the same point of spacetime -- that is, at the same place at the same instant. The reason is that in general relativity, we take very seriously the notion that a vector is a little arrow sitting at a particular point in spacetime. To compare vectors at different points of spacetime, we must carry one over to the other. The process of carrying a vector along a path without turning or stretching it is called `parallel transport'. When spacetime is curved, the result of parallel transport from one point to another depends on the path taken! In fact, this is the very definition of what it means for spacetime to be curved. Thus it is ambiguous to ask whether two particles have the same velocity vector unless they are at the same point of spacetime.
The only way I could make sense out of the OP (original post) was assuming that the OP meant "momentum" when it said "vectors". It's possible I misunderstood, of course. Regardless, all vectors (as the term is used in GR) have the properties that Baez describes regarding one's inability to add or even compare them unless they are at the same location.

This is one reason why the closest thing the universe has to a frame that is "at rest", the CMB frame, is not an inertial frame, but a series of different frames that are all moving away from one another.

It's probably also important to note that standard cosmological models assume the universe is infinite (or very very large, and that we are not near the edge). Of course the part we can actually observe (the observable universe) is finite.

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While such a frame, if it could be defined, would be interesting, it would not qualify as an absolute frame. An absolute frame is generally understood to imply that no other object is used to construct it. In this case, you are using many objects to construct your frame. So it's just an interesting relative frame.
I'm sure there are all sorts of complications I'm not thinking of, but if the vector sums did remain within a sphere somewhere in the universe, the center of that sphere wouldn't move relative to any observer.

shouldn't the sum be zero. or else it would be like the universe is moving somewhere.
I was thinking that it would be sort of like a brownian plot of a particle. The universe seems clumpy to a certain extent (as evidenced by CMBR pictures) so the vector sums would wander around a bit. It may be smooth enough however that the wandering sums stay within a defined and fairly small sphere (in relation to the total universe).

If you could define the sphere, then the center of that sphere could be said to be stationary relative to every other point in the universe. Any apparent motion of that point across the sky could be interpreted as the observer's motion relative to this point rather than the other way around.

vectors of what, of forces acting on them, of their displacements,of their velocities, of what exactly?
Displacements for given time.

What do you mean by "the vectors" (that's really loop quantum gravity's question). All relevent vectors: force, acceleration, velocity, momentum, are only defined relative to some frame of reference. Starting from a different frame of reference would give different vectors and so a different result for the "sum of all vectors".
I was starting with the premise that at any given time, the universe has a state that exists regardless of our ability to measure it.

For example: If astronomers were lucky enough to record the birth of a sun-like star, the exact instant when it's nuclear fires ignited, and if after performing spectral analysis, they determined that the star was 4 billion light years away, it would be reasonable to assume that the star still exists. The star would actually be 4 billion years old, not days or weeks.

So from this, we could say that the universe has a non-relativistic state. We can't measure that state, but we might be able to come up with a rough extrapolation by projecting known physical laws forward in time from the point of observation.

Some of the technical points regarding vectors in GR are rather,well, technical. I will give a source that points out that you can't add them together in GR the way you do in SR rather than talk about the details myself. See Baez's

http://math.ucr.edu/home/baez/einstein/node2.html" [Broken]

which also talks a little bit about "relative" vs "absolute" velocities. The following quote is from that URL.

It's probably also important to note that standard cosmological models assume the universe is infinite (or very very large, and that we are not near the edge). Of course the part we can actually observe (the observable universe) is finite.

What do you mean by "the vectors" (that's really loop quantum gravity's question). All relevent vectors: force, acceleration, velocity, momentum, are only defined relative to some frame of reference. Starting from a different frame of reference would give different vectors and so a different result for the "sum of all vectors".
After chewing on that for awhile...

If you define a set of points on a circle with a large radius from your frame (say, 5 billion light years). Select whatever particles are closest to these points to use as the origin. Sum all vectors from these points and due to the fact that some of these origin points are bound to be closer to the "edge" of the universe than others, over time, the sums from each point should display a definite bias.

Points closer to the "edge" of the universe would display a bias in the direction of the geometric center as the shortened vectors from the edge side would be overpowered by the longer vectors from the rest of the universe.

Comparing the bias for each of the origin points should indicate roughly where the geometric center of the universe is and where the edge is. If you could find the center then it could be used as "the mother of all reference frames" for all distance and time measurements.

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pervect
Staff Emeritus
I'm sure there are all sorts of complications I'm not thinking of, but if the vector sums did remain within a sphere somewhere in the universe, the center of that sphere wouldn't move relative to any observer.
The problem is that there actually isn't any such vector sum mathematically defined, as I mentioned and my link mentioned.

No, I only gave a very simple scenario and asked you to apply on where exactly is this "magical frame" in which the "sum be zero". Are you saying that in this that very simple universe consisting of just 2 end masses, you cannot show such a thing?
I am saying that if you could add impulses instead of velocities, you would successfully figure out "the magic frame".

ZapperZ
Staff Emeritus
I am saying that if you could add impulses instead of velocities, you would successfully figure out "the magic frame".
Then show me using that very simple scenario that I've just described.

Zz.

I have a mass at the origin of some coordinate system. At t=0, it explodes into 2 pieces, A and B, going in opposite direction. A and B do not have the same mass, and do not have the same speed.
If a mass was at rest before explosion, we're already in that frame due to this magical equation. If not, we should switch to frame of obserer co-moving with your mass. What you want me to show here? p(A) = -p(B)?

ZapperZ
Staff Emeritus
If a mass was at rest before explosion, we're already in that frame due to this magical equation. If not, we should switch to frame of obserer co-moving with your mass. What you want me to show here? p(A) = -p(B)?
So then you would use ONLY the momentum conservation to pick out your "magic frame" in this simple universe?

Zz.

well if we ground its "magicalness" on the notion that, taken as whole, it does not move anywhere, then yes, why not.

imagine an observer that has added all moments (what a hell is right english word for it, btw, I thought it's "impulses") of all things around himself (and his own 0 vector) and found that sum is not zero. doesn't it suggest him that the stuff-as-whole is moving somewhere? and if so, then where?

ZapperZ
Staff Emeritus
well if we ground its "magicalness" on the notion that, taken as whole, it does not move anywhere, then yes, why not.
But that's the MAGIC word of the day... IF we give somehow the "magicalness" of a frame of reference that has zero total momentum. Note that if I were to add only the velocity, I would not get a net sum to be zero and in fact, I will have to shift to a different inertial frame to get that, no? And if I were you add the displacement vector, I in fact may not get even any!

Thus, using this simple universe (which actually has nothing to do with the origin of our universe since this simple universe already has the space and time "frame" to use), you have to convince the OP (who wants to add "vectors" of the generic kind) that he/she has to use only ONE criteria out of many to do such a summation, and that this criteria actually has some fundamental underlying significance.

Zz.

It is not possible to find an absolute reference frame that is beyond the intellect. An observer may find what he thinks to be an absolute reference frame, but it cannot be concluded as absolute since it is surpassed by the intellect that found it. It is perfectly logical to conclude in theory that the intellect is the absolute reference frame. So I'm sure there will be much to discuss and I'll be itching to see your reply.

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