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#21
19-04-2011, 09:55 AM
 CraigS Unpredictable Join Date: Jul 2010 Location: Australia Posts: 3,022
Hey Steven;

What makes them/why are they called 'discrete' ?

Wiki says:

Quote:
 A discrete symmetry is a symmetry that describes non-continuous changes in a system. For example, a square possesses discrete rotational symmetry, as only rotations by multiples of right angles will preserve the square's original appearance. Discrete symmetries sometimes involve some type of 'swapping', these swaps usually being called reflections or interchanges. In theoretical physics, a discrete symmetry is a symmetry under the transformations of a discrete group—e.g. a topological group with a discrete topology whose elements form a finite or a countable set.
So, from that, I guess the discrete transformational group in this instance, would be: Charge, Parity and Time ? (A finite, countable set). Would these be the properties of the wavefunction of the particle ?

And thus would gravity and anti-gravity, be properties of the interactions between the particles and is thus belongs to continuous symmetry ?

Cheers

Last edited by CraigS; 19-04-2011 at 10:08 AM.
#22
19-04-2011, 10:37 AM
 renormalised (Carl) No More Infinities Join Date: Apr 2008 Location: Townsville Posts: 9,546

Quote:
 Originally Posted by CraigS Folks; Lensing results in path, and hence image, distortion of the background object. There is no single focussing point. There is a line along which light is bent towards, but this only indicates the centre of mass of the 'lens'. There is no 'convergence' and thus, no 'divergence'. As such, 'divergence' of the light paths, if the 'lens' is composed of anti-matter would be pure conjecture, which I'm happy to challenge. Cheers
There's was no mention of any focusing point at all. Just divergent paths due to a repulsive force being propagated within spacetime. Whether it's gravity or "anti-gravity" that is being observed, so long as the phenomenon is conserving CPT symmetry (for that system) there is no violation of the physical laws. Even if it looks "dodgy" to our experience.

Remember, a gravitational field bends light towards the centre of gravity because spacetime bends inwards towards that centre. Any repulsive force, i.e. antigravity, would act in the opposite manner and you would get divergent light paths through that section of spacetime (in our estimation). This is all happening on the proviso that the negative field exists around discrete objects and is not a function of expanding spacetime (i.e. acceleration due to "dark energy"). The fact that they haven't observed anything like this in reality says that it probably doesn't occur.

The only way for a gravitational lens to look exactly the same for both regions is if there was an instantaneous switch in CPT symmetry for any photons crossing from one region to another, otherwise we'd be getting all sorts of weird effects.

Last edited by renormalised; 19-04-2011 at 11:24 AM.
#23
19-04-2011, 11:03 AM
 renormalised (Carl) No More Infinities Join Date: Apr 2008 Location: Townsville Posts: 9,546

Quote:
 Originally Posted by sjastro ....The problem I see with this model is that there is no explanation as to why "dark energy" is increasing. Due to the metric expansion of the Universe one would expect the effects of anti-gravity, like gravity, to decrease as the density of the Universe decreases with time. Regards Steven
I think this is where they (physicists) get people confused because they normally don't clarify what they say. People think when they say "dark energy is increasing" that the actual quantity of dark energy is becoming larger. Since the universe, we believe, is a closed system, such an increase would violate the laws of physics. So, it's really just an increase in its influence when compared to the influence of gravity as the universe expands.
#24
19-04-2011, 12:10 PM
 sjastro Registered User Join Date: Jun 2007 Posts: 2,191
Quote:
 Originally Posted by CraigS Hey Steven; What makes them/why are they called 'discrete' ? Wiki says: A discrete symmetry is a symmetry that describes non-continuous changes in a system. For example, a square possesses discrete rotational symmetry, as only rotations by multiples of right angles will preserve the square's original appearance. Discrete symmetries sometimes involve some type of 'swapping', these swaps usually being called reflections or interchanges. In theoretical physics, a discrete symmetry is a symmetry under the transformations of a discrete group—e.g. a topological group with a discrete topology whose elements form a finite or a countable set. So, from that, I guess the discrete transformational group in this instance, would be: Charge, Parity and Time ? (A finite, countable set). Would these be the properties of the wavefunction of the particle ? And thus would gravity and anti-gravity, be properties of the interactions between the particles and is thus belongs to continuous symmetry ? Cheers
Craig you are correct that the interaction is a function of continuous symmetry but it tells us little about the particles themselves.
This is where discrete symmetry comes into the picture.

A particle's wavefunction can be defined by its (discrete) quantum numbers. These quantum numbers are the result of symmetry operations on the wavefunction. Particles can be grouped into common symmetry operations.
Like the conservation of energy and mass, it was expected the symmetry operations within each group would be similarly conserved.

For example parity is conserved in electromagnetic interactions. Two electrons of even parity remain even after a photon is exchanged.
In the case of the weak interaction parity is not conserved.

The CPT theorem states that by applying the discrete symmetries of charge conjugation (C), parity (P) and time reversal (T), one has an exact symmetry and the laws of physics are invariant.

Regards

Steven
#25
19-04-2011, 12:17 PM
 mswhin63 (Malcolm) Registered User Join Date: May 2009 Location: Warnbro, Western Australia Posts: 2,983
Just curious that if normal matter disperses electromagnetic radiation that allows us to detect normal matter.
How does Antimatter work in relation to electromagnetic spectrum?
#26
19-04-2011, 12:17 PM
 sjastro Registered User Join Date: Jun 2007 Posts: 2,191
Quote:
 Originally Posted by renormalised I think this is where they (physicists) get people confused because they normally don't clarify what they say. People think when they say "dark energy is increasing" that the actual quantity of dark energy is becoming larger. Since the universe, we believe, is a closed system, such an increase would violate the laws of physics. So, it's really just an increase in its influence when compared to the influence of gravity as the universe expands.
Yes "increasing dark energy" is a misnomer as the effects of dark energy becomes more apparent with decreasing density.

Regards

Steven
#27
19-04-2011, 12:38 PM
 CraigS Unpredictable Join Date: Jul 2010 Location: Australia Posts: 3,022
Hmm .. interesting .. thanks for that, Steven.

For my understanding, it seems this may come back to what we know ie: quantum (discreteness) theory, works cleanly for discrete particles.

The concept of a 'Field', (ie: resulting from interactions between particles), which is covered by continuous symmetry groupings, can be incorporated into the quantum world (QFT), with all of the complexities and issues arising therein. I can see now, how this theory may be playing in that region. Continuous anything fitting into the quantum world, would seemingly require special handling, and thus may fit into its own category.

And within that given category, symmetry of behaviour exists (and the laws of physics remain unchanged).

(I just made all that up … I hope its along the right lines. Don't want to disrupt the thread too much .. so I'll let it drop and do some more reading on it.)

Cheers
#28
19-04-2011, 01:11 PM
 Robh (Rob) Registered User Join Date: Feb 2009 Location: Blue Mountains, Australia Posts: 1,219
Quote:
 Originally Posted by CraigS Folks; Lensing results in path, and hence image, distortion of the background object. There is no single focussing point. There is a line along which light is bent towards, but this only indicates the centre of mass of the 'lens'. There is no 'convergence' and thus, no 'divergence'.
Craig,

Let's say I can piggyback a photon travelling through space. To all intents and purposes, me and my photon appear to be driving a nice straight path through space. However, to a distant observer of the photon, when it is in the presence of a massive body, it is following a geodesic path or curve in the surrounding empty black space. We cannot actually see the space curvature without the use of a travelling particle or body within it. Thus, it appears that the light from a star can be "bent" around the rim of an eclipsed sun.
Now consider several distant galaxies lensed by a massive foreground object. They appear distorted but aligned in an annular region surrounding the massive foreground object. The light from these is seen from the Earth only because it is sent in our direction.
You have to remember that lensed galaxies are not single points and the light from all the constituent points of each galaxy must be sent our way. If we were any closer or further away, this annular region could most likely bypass us and not be seen. In this sense, we are at the focal point of observation.
We can say that the light from the galactic images, converge towards the Earth from around the site of the massive body. Conversely, if anti-matter has the effect of repulsing "normal" matter, then the light would diverge away from the observer's line of sight.
If geodesic paths can be thought of in geometrical terms, I see no reason that these paths can't be thought of as convergent or divergent from a distant point.

Regards, Rob
#29
19-04-2011, 02:13 PM
 CraigS Unpredictable Join Date: Jul 2010 Location: Australia Posts: 3,022
Hi Rob;

I can't agree with some bits and my reasons are below. .. Perhaps we just have different wording interpretations ?
The different principles I'm basing mine on, are as follows.
(If I've misinterpreted these, please feel free to let me know):

Quote:
 Originally Posted by Robh Craig, Now consider several distant galaxies lensed by a massive foreground object. They appear distorted but aligned in an annular region surrounding the massive foreground object. The light from these is seen from the Earth only because it is sent in our direction.
The light, clearly, is radiated spherically from the source. We are on the lens corrected light path, otherwise would see nothing of the background image.

The shape of the distortion in the image we see, is a function of:

i) the mass distribution of the lens and, (of course);
ii) the shape of the object we're looking at and;
iii) the position of the background object relative to the position of the intervening lens.

Interestingly, there are different effects moving from the centre of mass, (of the lens), outwards, varying from rings, to arcs to multiple images.

Time delays also appear between multiple images, (in the case of multiple images), from the same source, because of optical path length variations and the Shapiro effect. If the source spectrum varies over time, variations will be observed in the multiple images, also.

A typical grav lens, can appear to magnify parts of, and distort very distant sources, moreso than sources closer to the lens.

Quote:
 Originally Posted by Robh You have to remember that lensed galaxies are not single points and the light from all the constituent points of each galaxy must be sent our way. If we were any closer or further away, this annular region could most likely bypass us and not be seen. In this sense, we are at the focal point of observation. We can say that the light from the galactic images, converge towards the Earth from around the site of the massive body.
I would say the only reason we see the object in the first place, is because Earth coincidentally, lies along the 'focal line' of the lens (as I mentioned before). There is no 'focal point'. 'Focal point' in optics has a very specific meaning. It is where light rays converge. There is no convergence. We merely lie along the path of propagation of the 'lensed' light. There is no 'convergence' and thus, there is no 'divergence'.

This is actually the distinguishing feature of a gravitational lens, and differentiates it from an optical lens.

(Actually, unlike an optical lens, the maximum bending occurs closest to the centre of the grav lens, and the minimum bending occurs furthest from the the centre of mass of the lens, also).

Quote:
 Originally Posted by Robh Conversely, if anti-matter has the effect of repulsing "normal" matter, then the light would diverge away from the observer's line of sight.
As Steven says (and I agree with him):
Quote:
 Originally Posted by sjastro Because of CPT symmetry, an observer would see the same lensing effect irrespective if the lens is made from matter or antimatter. The null geodesic of the photon (or antiphoton) must remain the same for the laws of physics to remain invariant otherwise the symmetry is violated.
Quote:
 Originally Posted by Robh If geodesic paths can be thought of in geometrical terms, I see no reason that these paths can't be thought of as convergent or divergent from a distant point.
See Steven's words above.

Cheers
#30
19-04-2011, 06:44 PM
 renormalised (Carl) No More Infinities Join Date: Apr 2008 Location: Townsville Posts: 9,546
Quote:
 I would say the only reason we see the object in the first place, is because Earth coincidentally, lies along the 'focal line' of the lens (as I mentioned before). There is no 'focal point'. 'Focal point' in optics has a very specific meaning. It is where light rays converge. There is no convergence. We merely lie along the path of propagation of the 'lensed' light. There is no 'convergence' and thus, there is no 'divergence'. This is actually the distinguishing feature of a gravitational lens, and differentiates it from an optical lens. (Actually, unlike an optical lens, the maximum bending occurs closest to the centre of the grav lens, and the minimum bending occurs furthest from the the centre of mass of the lens, also).
Craig, you still don't get it. Yes, there is a focal line produced by the gravitational lens (due to the way it bends the light), but that focal line is not parallel to the direction the light travels (which is what I think you're imagining). It's perpendicular to the incident light rays, i.e. it's like a focal point that's been stretched out into a line. That's why you get either circular rings/arcs or multiple images depending on the geometry of the placement of the objects. The light rays bending at the lens must converge to the focal line, otherwise you wouldn't see anything.

In our example, if you have photons that remain as normal photons and they pass through a region of antimatter, according to the paper since they have a different CPT symmetry to the region they're passing through, unless they change their symmetry to match that of the region (i.e. they become antiphotons), they will move in divergent paths away from any large mass/lens because of the "repulsion" they feel (they travel along a divergent spacetime curve in their experience). You don't get a focal line at all.

Last edited by renormalised; 19-04-2011 at 06:56 PM.
#31
19-04-2011, 08:04 PM
 Robh (Rob) Registered User Join Date: Feb 2009 Location: Blue Mountains, Australia Posts: 1,219
Quote:
 Originally Posted by CraigS I would say the only reason we see the object in the first place, is because Earth coincidentally, lies along the 'focal line' of the lens (as I mentioned before). There is no 'focal point'. 'Focal point' in optics has a very specific meaning. It is where light rays converge. There is no convergence. We merely lie along the path of propagation of the 'lensed' light. There is no 'convergence' and thus, there is no 'divergence'. This is actually the distinguishing feature of a gravitational lens, and differentiates it from an optical lens.
Hi Craig,

Firstly, let me say that I agree with you that gravitational lensing has a different mode of operation to classical optical lens systems.
There are differences but there are also similarities. And some of the terminology from classical optics does imply a similar meaning in the context of gravity-based lensing even if the mode of operation is different.

I'll concede on the divergence issue as this depends on properties of anti-matter that I can't comment on. If anti-matter does repel normal matter then many new doors are opened.

However, as to the issues on convergence and focus, consider the attached diagram of a symmetrical gravitational lens.
Every massive body is capable of lensing. In fact, given the right circumstances, this lensing can take the form of a ring of multiple images of the far body. In your argument, you are looking specifically at an observer at point A that sees light that has travelled on a specific path (or geodesic) from the far galaxy shown. The observer at A has no sense of the convergence of this light, nor of any specific focal point.
Now consider an observer on the Earth. This observer sees at least two images of the far galaxy, image 1 and image 2. The reason he/she sees these is that the paths of light from the distance galaxy converge to a point on the Earth. This is in fact the focal point for the gravitational lens. Every symmetrical lens will have a specific focal point. The focal point will depend on several factors e.g. the distance of the far galaxy and the mass of the lensing body.
Now consider an observer at B. He/she sees neither image 1 nor 2 as the focal point for this model is further out i.e the Earth.

This is of course an ideal situation. Many lenses are not symmetric and there will perhaps be several focal points (somewhat like astigmatism in classical optics).
And, although a different mode of operation, we can also use the term magnification with regard to gravitational lensing.

Regards, Rob.
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Last edited by Robh; 20-04-2011 at 09:28 AM. Reason: Images are numbered
#32
20-04-2011, 07:32 AM
 sjastro Registered User Join Date: Jun 2007 Posts: 2,191
A couple of issues here.

(1) Since photons are there own anti-particles a photon (antiphoton) will behave the same in the field of matter (antimatter). In other words both will travel along null geodesics.

(2) I'm not sure why it is assumed antimatter will produce a "divergent" spacetime.

Consider the spacetime around a large mass antimatter object. A small mass antimatter object will move in a geodesic path equivalent to both objects being made from matter. In other words spacetime is "convergent".
Spacetime is still "convergent" if we replace the small antimatter mass with a small mass since spacetime curvature is determined by the larger mass.
What happens to spacetime if we have small antimatter and matter masses in the presence of the larger antimatter (or matter) mass?

For those that know GR if both masses are either antimatter or matter, Einstein field equations simply reduce to the Ricci tensor R(u,v)=0.

In the case of a large antimatter mass/ small matter mass (or vice versa) perhaps we should consider what happens if we have a large and small mass where both masses are carrying a postive or negative charge. We have a scenario that "resembles" the hypothetical matter/antimatter repulsive force.
In this case we a strong electromagnetic field acting with the gravitational field and a repulsive Lorentz force acting on the smaller mass.

The electromagnetic field becomes part of the field equations.
The field equations take the form G(u,v) = (-8*pi*G)/c ^2*T(u,v)+F(....)

G(u,v) is the Einstein tensor.
G is the gravitational constant.
T(u,v) is the matter energy tensor.
F(.....) is a long winded term for an electromagnetic tensor.

I would imagine the the repulsive force between matter and anti matter would be treated in a similar way.

Regards

Steven
#33
20-04-2011, 08:43 AM
 CraigS Unpredictable Join Date: Jul 2010 Location: Australia Posts: 3,022
Hi Rob;

Thank you for taking the time to draw and describe where you’re coming from. Much appreciated.

Fascinating.

As I highlighted in my conversation with Steven, I suppose we (meaning I), should evaluate this theory within the bounds it establishes for itself. Unfortunately, I have a feeling that the ‘lensing’ topic falls outside of those boundaries.

We know lensing exists, because we’ve observed it (ie: its now beyond a theoretical prediction). Its not mentioned in the paper. I suppose this is to be expected from a purely theoretical topic/paper. Curiously though, he specifically looks towards voids for finding anti-matter clumps, (of 'tens of Mpcs, no less !), which might support his theory. (This would be a practical, empirical step, which would then take it outside of theoretical boundaries).

How an anti-matter lens would form and remain stable, around some cluster/galaxy (object) etc, is difficult to envisage. Firstly, I believe that in all instances so far discovered, the foreground object is composed of normal matter. If anti-matter were to remain from the initial stages of formation, then what keeps it around the object ? What about where the normal matter comes within the proximity of the anti-matter ? Lagrange points would be everywhere, with both repulsive and attractive forces surrounding these points.

Ok, so lets imagine somehow, the forces cancel eachother and that’s what keeps the lens there. Ok, we somehow have a stable anti-matter grav lens in the midst of normal matter. I agree with Steven's approach of viewing the behaviour of this region, in the same way we'd view 'normal matter' field interactions. (What else do we have to go on ? )

(Incidentally, regardless of how the lens interacts with a photon, what we’d see from Earth, remains a function of the distribution of the anti-matter in the lens, the shape of the object and its distance from the lens. I think we’d still see the same patterns. Ie: rings, arcs, multiple images, etc. The intersecting photons could transit any region listed above, and result in any or all effects).

Ok. I understand the matters you raise on ‘focal point’. You hit the nail on the head in your words:

Quote:
 Originally Posted by Robh This is of course an ideal situation. Many lenses are not symmetric and there will perhaps be several focal points (somewhat like astigmatism in classical optics). And, although a different mode of operation, we can also use the term magnification with regard to gravitational lensing.
I agree with what you say (in an ideal thin lens situation). One of the main areas of interest about gravitational lenses, comes from the fact that they are far from ideal. The images we see from them, is very much a function of:

Quote:
 Originally Posted by CraigS The shape of the distortion in the image we see, is a function of: i) the mass distribution of the lens
There may be multiple ‘lenses’, quite possibly with none of them having any well defined ‘focal points’. (I use the term here, in its strictest definitional sense).

Interestingly, the author of the paper focuses more on the possibility that anti-matter may be a candidate for Dark Energy. He makes no mention of lenses, or of Dark Matter’s influences on galaxy rotation. In his conclusion, he gives a half-hearted comment:
Quote:
 These new cosmological scenarios could eliminate the uncomfortable presence of an unidentified dark energy, and maybe also of cosmological dark matter, which, according to the Lambda-CDM concordance model, would together represent more than the 95% of the Universe content.
It was us who brought up the lensing issue, and lensing effects are a much more complex than we might initially imagine.

Cheers & Rgds
#34
20-04-2011, 08:49 AM
 bojan amateur Join Date: Jul 2006 Location: Mt Waverley, VIC Posts: 3,690
Craig,
You can't ignore the lensing effect here (even if they did...). It is the effect of ANY mass concentration and it must be taken into account as one (only?) way of identification of such mass concentrations existence.

After all, this was the way dark matter was detected around some clusters of galaxies.
#35
20-04-2011, 08:52 AM
 CraigS Unpredictable Join Date: Jul 2010 Location: Australia Posts: 3,022
Quote:
 Originally Posted by sjastro (2) I'm not sure why it is assumed antimatter will produce a "divergent" spacetime. Consider the spacetime around a large mass antimatter object. A small mass antimatter object will move in a geodesic path equivalent to both objects being made from matter. In other words spacetime is "convergent". Spacetime is still "convergent" if we replace the small antimatter mass with a small mass since spacetime curvature is determined by the larger mass. What happens to spacetime if we have small antimatter and matter masses in the presence of the larger antimatter (or matter) mass?
Yep .. I'm with ya, man.

Using the deformed rubber sheet model, perhaps the spacetime 'dimple' around the anti-massive object, simply dimples in the opposite direction from that created by say, a normal matter object ? In either case, the effect we'd observe from Earth, would be the same ?

The interesting bit may be where the two fields interact .. and maybe this isn't all that interesting anyway … it happens all the time in electromagnetic fields.

Cheers
#36
20-04-2011, 08:56 AM
 CraigS Unpredictable Join Date: Jul 2010 Location: Australia Posts: 3,022
Quote:
 Originally Posted by bojan Craig, You can't ignore the lensing effect here. It is the effect of ANY mass concentration and it must be taken into account as one (only?) way of identification of such mass concentrations existence.
Yep. See my just made post.

I'm starting to feel like we're arguing over 'how many angels can dance on a pin-head', Bojan.

Cheers
#37
20-04-2011, 09:12 AM
 renormalised (Carl) No More Infinities Join Date: Apr 2008 Location: Townsville Posts: 9,546

Quote:
 Originally Posted by sjastro A couple of issues here. (1) Since photons are there own anti-particles a photon (antiphoton) will behave the same in the field of matter (antimatter). In other words both will travel along null geodesics. (2) I'm not sure why it is assumed antimatter will produce a "divergent" spacetime. Consider the spacetime around a large mass antimatter object. A small mass antimatter object will move in a geodesic path equivalent to both objects being made from matter. In other words spacetime is "convergent". Spacetime is still "convergent" if we replace the small antimatter mass with a small mass since spacetime curvature is determined by the larger mass. What happens to spacetime if we have small antimatter and matter masses in the presence of the larger antimatter (or matter) mass? For those that know GR if both masses are either antimatter or matter, Einstein field equations simply reduce to the Ricci tensor R(u,v)=0. In the case of a large antimatter mass/ small matter mass (or vice versa) perhaps we should consider what happens if we have a large and small mass where both masses are carrying a postive or negative charge. We have a scenario that "resembles" the hypothetical matter/antimatter repulsive force. In this case we a strong electromagnetic field acting with the gravitational field and a repulsive Lorentz force acting on the smaller mass. The electromagnetic field becomes part of the field equations. The field equations take the form G(u,v) = (-8*pi*G)/c ^2*T(u,v)+F(....) G(u,v) is the Einstein tensor. G is the gravitational constant. T(u,v) is the matter energy tensor. F(.....) is a long winded term for an electromagnetic tensor. I would imagine the the repulsive force between matter and anti matter would be treated in a similar way. Regards Steven
Normally, everything you have said would be the case, but what I and Rob said is what if the photons were behaving as normal photons and not as antiphotons, for whatever reasons, within that region of antimatter space, as the journal article mentioned. If there was this repulsive gravitational force present, because the CPT symmetry of those photons would be opposite to the region they were in, they would act in accordance with that...i.e. they would move in divergent paths within the antigravitational field (in their experience), away from the lensing mass. Off course, antiphotons would behave normally and you'd see the same results of the lensing that we would. However, that's not what we see, so the theory proposed is just a simple thought experiment and has no basis in observation.

Last edited by renormalised; 20-04-2011 at 09:39 AM.
#38
20-04-2011, 09:16 AM
 bojan amateur Join Date: Jul 2006 Location: Mt Waverley, VIC Posts: 3,690
Quote:
 Originally Posted by CraigS Why bother, I ask ? Cheers
Well, because, in light of what Steven wrote (photons behaving the same way in presence of mass, be it matter or antimatter) and the fact that no divergent lensing was detected, the whole theory (antimatter, universe, expansion and so on) doesn't hold water.. or so it seems to me.
#39
20-04-2011, 09:27 AM
 CraigS Unpredictable Join Date: Jul 2010 Location: Australia Posts: 3,022
Quote:
 Originally Posted by bojan Well, because, in light of what Steven wrote (photons behaving the same way in presence of mass, be it matter or antimatter) and the fact that no divergent lensing was detected, the whole theory (antimatter, universe, expansion and so on) doesn't hold water.. or so it seems to me.
Ok … seems we are all in violent agreement on the no 'divergent' lensing detected, and also that the theory should get the stuffing knocked out of it !

Done !

Cheers
#40
20-04-2011, 09:30 AM
 renormalised (Carl) No More Infinities Join Date: Apr 2008 Location: Townsville Posts: 9,546
I just thought of something interesting....if there was a region of space with a completely different CPT symmetry to our own, you could easily detect its presence. All because of the boundary conditions between us and them. Our spacetime would bend anomalously around the region of negative space....the Hubble flow in that direction would look strangely askew as space expanded around the negative spacetime.

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