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|
| Author |
Message |
Robert
science forum beginner
Joined: 17 Nov 2005
Posts: 41
|
 Posted: Sun Jun 11, 2006 6:42 pm Post subject:
Gravity - What is the cause (GR vs. QFT)?
|
|
|
As I understand it, Einstein's theory of General Relativity (GR) seems to
describe gravity as being caused by curved space-time alone. No gravitons
are necessary. However, quantum field theory is said to predict the
existence of a graviton (which is massless, like a photon) and it is through
the interaction of gravitons that gravity is produced.
On the surface it seems as if these are two totally imcompatible world
views. One has go to go. Well, in discussions here and elsewhere we always
get the same result. Some people say "Yes, these two views are really
imcompatible" while another groups saus "No, you're crazy, they are totally
compatible."
Umm, both groups can't be correct. I would it appreciate it if people would
look through the various answers to this question, and let me know what they
think?
One very interesting answer is here. Thoughts?
http://www.lns.cornell.edu/spr/1999-02/msg0014781.html
Re: Gravity: Wave-Particle vs Space-Time Warpage
Subject: Re: Gravity: Wave-Particle vs Space-Time Warpage
From: baez@galaxy.ucr.edu (john baez)
Date: 14 Feb 1999 00:00:00 GMT
Other answers came from a discussion on www.physicsforums.com. Some people
there answered that GR's model of a curved space causing gravity is totally
at odds with the graviton model of gravity. For instance:
selfAdjoint states:
"The graviton is a theoretical particle predicted by string theory but not
yet demonstrated to exist. If it exists and is the cause of gravity it will
do away with spacetime curvature and produce gravity the way the photon
carries electromagnetism. Then gravity would be a (quantum) force in your
sense."
"At the present time however, our best theory of gravity is Einstein's 1915
General Theory of Relativity. One of the basic propositions of that theory
is the Principle of Equivalence: On a sufficiantly small scale, it is
impossible to tell the difference between an imposed force and a
gravitational one. Notice that the shape is the shape of spacetime, not just
of space. Therefore a curved geodesic goes through time as well as space,
and by curving, causes those travelling along it to experience an
acceleration. Anything that produces an acceleration deserves the name
force, no?"
Nenad writes:
"...because if the graviton is found, then there is no curvature of space
time, the reson there is gravity will be because of the graviton. You cant
have both explaining the same thing."
However, some people come to exact opposite conclusion! They hold that the
GR model is compatible with the graviton model of gravity. For instance:
jtolliver writes:
| Quote: | yes, if the graviton is found, General Relativity will be wrong.
|
"Not really. Any lorentz-invariant interaction that preserves causality can
be described in terms of particles. GR satisfies those conditions.
Gravitational waves have many properties traditionally associated with
particles (If you pretend spacetime is flat and you add gravitational forces
to compensate), such as energy-momentum. Using curved space-time(the
technique traditionally used in GR), and using flat space-time with an
additional force that makes it act exactly as though it were curved(this was
the technique used in classical mechanics, except that that force didn't
quite make it act exactly as curved space-time) are just different ways of
looking at the same thing. The first way is much more convient
mathematically, and the second way doesn't really explain why we have this
additional force. The graviton's only look like particles when we assume
spacetime is flat. If we assume spacetime is curved we see it is really only
an effect of the curvature of spacetime, even though it looks exactly like a
particle."
pmb_phy writes:
....It is not the curvature of spacetime that causes gravitational
acceleration. Spacetime curvature causes two particles moving under to have
a relative acceleration between them, i.e. spacetime curvature causes tidal
accelerations. But you can have a gravitational force in the absense of
spacetime curvature."
| Quote: | The graviton is a theoretical particle predicted by string theory
but not yet demonstrated to exist.
|
It doesn't come from string theory. It comes from quantum gravity/quantum
field theory.
| Quote: | If it exists and is the cause of gravity it will do away
with spacetime curvature ...
|
That is incorrect. The graviton is responsible for producing gravitational
forces, not just tidal forces. Therefore one should aslo be able to detect
gravitons in a gravitational field even when the spacetime is flat. The
graviton, if it exists, will have a relative existance in that sense.
| Quote: | yes, if the graviton is found, General Relativity will be wrong.
if the graviton is found, then there is no curvature of space time,
the reson there is gravity will be because of the graviton. You cant
have both explaining the same thing.
|
That is very much incorrect. You can most certainly have both. If the
graviton is detected then we will have the mechanism behind GR. Gravitons
are certainly not inconsistent with general relativity.
| Quote: | Couldnt you say the graviton cause the curvature of spacetime...lol
|
Absolutely. That is 100% correct.
Gravity is not like other forces like the electric of magnetic forces. The
gravitational force is an inertial force where the others aren't.
---
Ok, so which view is correct? (References to peer-reviewed lit, or books by
respected authors, would also be appreciated.)
Thanks,
Robert |
|
| Back to top |
|
 |
sarah
science forum beginner
Joined: 19 Apr 2005
Posts: 5
|
| Posted: Mon Jun 12, 2006 4:28 am Post subject:
Re: Gravity - What is the cause (GR vs. QFT)?
|
|
|
Robert wrote:
| Quote: | As I understand it, Einstein's theory of General Relativity (GR) seems to
describe gravity as being caused by curved space-time alone. No gravitons
are necessary. However, quantum field theory is said to predict the
existence of a graviton (which is massless, like a photon) and it is through
the interaction of gravitons that gravity is produced.
On the surface it seems as if these are two totally imcompatible world
views. One has go to go. Well, in discussions here and elsewhere we always
get the same result. Some people say "Yes, these two views are really
imcompatible" while another groups saus "No, you're crazy, they are totally
compatible."
Umm, both groups can't be correct. I would it appreciate it if people would
look through the various answers to this question, and let me know what they
think?
One very interesting answer is here. Thoughts?
http://www.lns.cornell.edu/spr/1999-02/msg0014781.html
Re: Gravity: Wave-Particle vs Space-Time Warpage
Subject: Re: Gravity: Wave-Particle vs Space-Time Warpage
From: baez@galaxy.ucr.edu (john baez)
Date: 14 Feb 1999 00:00:00 GMT
Other answers came from a discussion on www.physicsforums.com. Some people
there answered that GR's model of a curved space causing gravity is totally
at odds with the graviton model of gravity. For instance:
selfAdjoint states:
"The graviton is a theoretical particle predicted by string theory but not
yet demonstrated to exist. If it exists and is the cause of gravity it will
do away with spacetime curvature and produce gravity the way the photon
carries electromagnetism. Then gravity would be a (quantum) force in your
sense."
"At the present time however, our best theory of gravity is Einstein's 1915
General Theory of Relativity. One of the basic propositions of that theory
is the Principle of Equivalence: On a sufficiantly small scale, it is
impossible to tell the difference between an imposed force and a
gravitational one. Notice that the shape is the shape of spacetime, not just
of space. Therefore a curved geodesic goes through time as well as space,
and by curving, causes those travelling along it to experience an
acceleration. Anything that produces an acceleration deserves the name
force, no?"
Nenad writes:
"...because if the graviton is found, then there is no curvature of space
time, the reson there is gravity will be because of the graviton. You cant
have both explaining the same thing."
However, some people come to exact opposite conclusion! They hold that the
GR model is compatible with the graviton model of gravity. For instance:
jtolliver writes:
yes, if the graviton is found, General Relativity will be wrong.
"Not really. Any lorentz-invariant interaction that preserves causality can
be described in terms of particles. GR satisfies those conditions.
Gravitational waves have many properties traditionally associated with
particles (If you pretend spacetime is flat and you add gravitational forces
to compensate), such as energy-momentum. Using curved space-time(the
technique traditionally used in GR), and using flat space-time with an
additional force that makes it act exactly as though it were curved(this was
the technique used in classical mechanics, except that that force didn't
quite make it act exactly as curved space-time) are just different ways of
looking at the same thing. The first way is much more convient
mathematically, and the second way doesn't really explain why we have this
additional force. The graviton's only look like particles when we assume
spacetime is flat. If we assume spacetime is curved we see it is really only
an effect of the curvature of spacetime, even though it looks exactly like a
particle."
pmb_phy writes:
...It is not the curvature of spacetime that causes gravitational
acceleration. Spacetime curvature causes two particles moving under to have
a relative acceleration between them, i.e. spacetime curvature causes tidal
accelerations. But you can have a gravitational force in the absense of
spacetime curvature."
The graviton is a theoretical particle predicted by string theory
but not yet demonstrated to exist.
It doesn't come from string theory. It comes from quantum gravity/quantum
field theory.
If it exists and is the cause of gravity it will do away
with spacetime curvature ...
That is incorrect. The graviton is responsible for producing gravitational
forces, not just tidal forces. Therefore one should aslo be able to detect
gravitons in a gravitational field even when the spacetime is flat. The
graviton, if it exists, will have a relative existance in that sense.
yes, if the graviton is found, General Relativity will be wrong.
if the graviton is found, then there is no curvature of space time,
the reson there is gravity will be because of the graviton. You cant
have both explaining the same thing.
That is very much incorrect. You can most certainly have both. If the
graviton is detected then we will have the mechanism behind GR. Gravitons
are certainly not inconsistent with general relativity.
Couldnt you say the graviton cause the curvature of spacetime...lol
Absolutely. That is 100% correct.
Gravity is not like other forces like the electric of magnetic forces. The
gravitational force is an inertial force where the others aren't.
---
Ok, so which view is correct? (References to peer-reviewed lit, or books by
respected authors, would also be appreciated.)
Thanks,
Robert
|
who is to say gravity is not caused by particle or by curve of space
time
much like energy and mass are interchangable parhaps in some form
gravity can be thought of as energy and can exist in many forms |
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|
|
<miltonpugh@sbcglobal.
science forum beginner
Joined: 18 Sep 2005
Posts: 21
|
| Posted: Tue Jun 27, 2006 2:33 am Post subject:
Re: Gravity - What is the cause (GR vs. QFT)?
|
|
|
"Robert" <rkscience100@NOSPAM.yahoo.REMOVECAPS.com> wrote in message
news:xuZig.244$2R.123@trndny02...
| Quote: | As I understand it, Einstein's theory of General Relativity (GR) seems to
describe gravity as being caused by curved space-time alone. No gravitons
are necessary. However, quantum field theory is said to predict the
existence of a graviton (which is massless, like a photon) and it is
through
the interaction of gravitons that gravity is produced.
On the surface it seems as if these are two totally imcompatible world
views. One has go to go. Well, in discussions here and elsewhere we always
get the same result. Some people say "Yes, these two views are really
imcompatible" while another groups saus "No, you're crazy, they are
totally
compatible."
Umm, both groups can't be correct. I would it appreciate it if people
would
look through the various answers to this question, and let me know what
they
think?
One very interesting answer is here. Thoughts?
http://www.lns.cornell.edu/spr/1999-02/msg0014781.html
Re: Gravity: Wave-Particle vs Space-Time Warpage
Subject: Re: Gravity: Wave-Particle vs Space-Time Warpage
From: baez@galaxy.ucr.edu (john baez)
Date: 14 Feb 1999 00:00:00 GMT
Other answers came from a discussion on www.physicsforums.com. Some people
there answered that GR's model of a curved space causing gravity is
totally
at odds with the graviton model of gravity. For instance:
selfAdjoint states:
"The graviton is a theoretical particle predicted by string theory but not
yet demonstrated to exist. If it exists and is the cause of gravity it
will
do away with spacetime curvature and produce gravity the way the photon
carries electromagnetism. Then gravity would be a (quantum) force in your
sense."
"At the present time however, our best theory of gravity is Einstein's
1915
General Theory of Relativity. One of the basic propositions of that theory
is the Principle of Equivalence: On a sufficiantly small scale, it is
impossible to tell the difference between an imposed force and a
gravitational one. Notice that the shape is the shape of spacetime, not
just
of space. Therefore a curved geodesic goes through time as well as space,
and by curving, causes those travelling along it to experience an
acceleration. Anything that produces an acceleration deserves the name
force, no?"
Nenad writes:
"...because if the graviton is found, then there is no curvature of space
time, the reson there is gravity will be because of the graviton. You cant
have both explaining the same thing."
However, some people come to exact opposite conclusion! They hold that the
GR model is compatible with the graviton model of gravity. For instance:
jtolliver writes:
yes, if the graviton is found, General Relativity will be wrong.
"Not really. Any lorentz-invariant interaction that preserves causality
can
be described in terms of particles. GR satisfies those conditions.
Gravitational waves have many properties traditionally associated with
particles (If you pretend spacetime is flat and you add gravitational
forces
to compensate), such as energy-momentum. Using curved space-time(the
technique traditionally used in GR), and using flat space-time with an
additional force that makes it act exactly as though it were curved(this
was
the technique used in classical mechanics, except that that force didn't
quite make it act exactly as curved space-time) are just different ways of
looking at the same thing. The first way is much more convient
mathematically, and the second way doesn't really explain why we have this
additional force. The graviton's only look like particles when we assume
spacetime is flat. If we assume spacetime is curved we see it is really
only
an effect of the curvature of spacetime, even though it looks exactly like
a
particle."
pmb_phy writes:
...It is not the curvature of spacetime that causes gravitational
acceleration. Spacetime curvature causes two particles moving under to
have
a relative acceleration between them, i.e. spacetime curvature causes
tidal
accelerations. But you can have a gravitational force in the absense of
spacetime curvature."
The graviton is a theoretical particle predicted by string theory
but not yet demonstrated to exist.
It doesn't come from string theory. It comes from quantum gravity/quantum
field theory.
If it exists and is the cause of gravity it will do away
with spacetime curvature ...
That is incorrect. The graviton is responsible for producing gravitational
forces, not just tidal forces. Therefore one should aslo be able to detect
gravitons in a gravitational field even when the spacetime is flat. The
graviton, if it exists, will have a relative existance in that sense.
yes, if the graviton is found, General Relativity will be wrong.
if the graviton is found, then there is no curvature of space time,
the reson there is gravity will be because of the graviton. You cant
have both explaining the same thing.
That is very much incorrect. You can most certainly have both. If the
graviton is detected then we will have the mechanism behind GR. Gravitons
are certainly not inconsistent with general relativity.
Couldnt you say the graviton cause the curvature of spacetime...lol
Absolutely. That is 100% correct.
Gravity is not like other forces like the electric of magnetic forces. The
gravitational force is an inertial force where the others aren't.
---
Ok, so which view is correct? (References to peer-reviewed lit, or books
by
respected authors, would also be appreciated.)
Thanks,
Robert
|
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| Back to top |
|
|
<miltonpugh@sbcglobal.
science forum beginner
Joined: 18 Sep 2005
Posts: 21
|
| Posted: Tue Jun 27, 2006 2:34 am Post subject:
Re: Gravity - What is the cause (GR vs. QFT)?
|
|
|
In wysiwyg physical world there are dedicated fields
"Robert" <rkscience100@NOSPAM.yahoo.REMOVECAPS.com> wrote in message
news:xuZig.244$2R.123@trndny02...
| Quote: | As I understand it, Einstein's theory of General Relativity (GR) seems to
describe gravity as being caused by curved space-time alone. No gravitons
are necessary. However, quantum field theory is said to predict the
existence of a graviton (which is massless, like a photon) and it is
through
the interaction of gravitons that gravity is produced.
On the surface it seems as if these are two totally imcompatible world
views. One has go to go. Well, in discussions here and elsewhere we always
get the same result. Some people say "Yes, these two views are really
imcompatible" while another groups saus "No, you're crazy, they are
totally
compatible."
Umm, both groups can't be correct. I would it appreciate it if people
would
look through the various answers to this question, and let me know what
they
think?
One very interesting answer is here. Thoughts?
http://www.lns.cornell.edu/spr/1999-02/msg0014781.html
Re: Gravity: Wave-Particle vs Space-Time Warpage
Subject: Re: Gravity: Wave-Particle vs Space-Time Warpage
From: baez@galaxy.ucr.edu (john baez)
Date: 14 Feb 1999 00:00:00 GMT
Other answers came from a discussion on www.physicsforums.com. Some people
there answered that GR's model of a curved space causing gravity is
totally
at odds with the graviton model of gravity. For instance:
selfAdjoint states:
"The graviton is a theoretical particle predicted by string theory but not
yet demonstrated to exist. If it exists and is the cause of gravity it
will
do away with spacetime curvature and produce gravity the way the photon
carries electromagnetism. Then gravity would be a (quantum) force in your
sense."
"At the present time however, our best theory of gravity is Einstein's
1915
General Theory of Relativity. One of the basic propositions of that theory
is the Principle of Equivalence: On a sufficiantly small scale, it is
impossible to tell the difference between an imposed force and a
gravitational one. Notice that the shape is the shape of spacetime, not
just
of space. Therefore a curved geodesic goes through time as well as space,
and by curving, causes those travelling along it to experience an
acceleration. Anything that produces an acceleration deserves the name
force, no?"
Nenad writes:
"...because if the graviton is found, then there is no curvature of space
time, the reson there is gravity will be because of the graviton. You cant
have both explaining the same thing."
However, some people come to exact opposite conclusion! They hold that the
GR model is compatible with the graviton model of gravity. For instance:
jtolliver writes:
yes, if the graviton is found, General Relativity will be wrong.
"Not really. Any lorentz-invariant interaction that preserves causality
can
be described in terms of particles. GR satisfies those conditions.
Gravitational waves have many properties traditionally associated with
particles (If you pretend spacetime is flat and you add gravitational
forces
to compensate), such as energy-momentum. Using curved space-time(the
technique traditionally used in GR), and using flat space-time with an
additional force that makes it act exactly as though it were curved(this
was
the technique used in classical mechanics, except that that force didn't
quite make it act exactly as curved space-time) are just different ways of
looking at the same thing. The first way is much more convient
mathematically, and the second way doesn't really explain why we have this
additional force. The graviton's only look like particles when we assume
spacetime is flat. If we assume spacetime is curved we see it is really
only
an effect of the curvature of spacetime, even though it looks exactly like
a
particle."
pmb_phy writes:
...It is not the curvature of spacetime that causes gravitational
acceleration. Spacetime curvature causes two particles moving under to
have
a relative acceleration between them, i.e. spacetime curvature causes
tidal
accelerations. But you can have a gravitational force in the absense of
spacetime curvature."
The graviton is a theoretical particle predicted by string theory
but not yet demonstrated to exist.
It doesn't come from string theory. It comes from quantum gravity/quantum
field theory.
If it exists and is the cause of gravity it will do away
with spacetime curvature ...
That is incorrect. The graviton is responsible for producing gravitational
forces, not just tidal forces. Therefore one should aslo be able to detect
gravitons in a gravitational field even when the spacetime is flat. The
graviton, if it exists, will have a relative existance in that sense.
yes, if the graviton is found, General Relativity will be wrong.
if the graviton is found, then there is no curvature of space time,
the reson there is gravity will be because of the graviton. You cant
have both explaining the same thing.
That is very much incorrect. You can most certainly have both. If the
graviton is detected then we will have the mechanism behind GR. Gravitons
are certainly not inconsistent with general relativity.
Couldnt you say the graviton cause the curvature of spacetime...lol
Absolutely. That is 100% correct.
Gravity is not like other forces like the electric of magnetic forces. The
gravitational force is an inertial force where the others aren't.
---
Ok, so which view is correct? (References to peer-reviewed lit, or books
by
respected authors, would also be appreciated.)
Thanks,
Robert
|
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|
|
<miltonpugh@sbcglobal.
science forum beginner
Joined: 18 Sep 2005
Posts: 21
|
| Posted: Tue Jun 27, 2006 2:48 am Post subject:
Re: Gravity - What is the cause (GR vs. QFT)?
|
|
|
Dedicated fields such as gravity and magnetic fields do not seem to have a
simple common cause, or any simple cause for either field. Not included in
wysiwyg physics are Ampere's dynamic electrical fields.
when a charged partical in motion in found in a dynamic electrical field, an
electrical squeeze play occurs causing the partical to seek a new path of
least resistance. This action is a re-direction of the particals own
inertia.
As different attributes of the dynamic electrical field engage with those of
the charged partical, action at a distance occures, but not from contiguous
physical linkage. The motion (force) is developed only locally by the source
and target materials.
Only dynamic electrical fields need bridge the gap.
The dynamic electrical field of a bar magnet is tangential to the bar and is
clockwise as you view the north pole of the magnet.
Read Ampere, All of it, especially where he talks about the westbound
dynamic electrical field of the earth. Lee Pugh
"Robert" <rkscience100@NOSPAM.yahoo.REMOVECAPS.com> wrote in message
news:xuZig.244$2R.123@trndny02...
| Quote: | As I understand it, Einstein's theory of General Relativity (GR) seems to
describe gravity as being caused by curved space-time alone. No gravitons
are necessary. However, quantum field theory is said to predict the
existence of a graviton (which is massless, like a photon) and it is
through
the interaction of gravitons that gravity is produced.
On the surface it seems as if these are two totally imcompatible world
views. One has go to go. Well, in discussions here and elsewhere we always
get the same result. Some people say "Yes, these two views are really
imcompatible" while another groups saus "No, you're crazy, they are
totally
compatible."
Umm, both groups can't be correct. I would it appreciate it if people
would
look through the various answers to this question, and let me know what
they
think?
One very interesting answer is here. Thoughts?
http://www.lns.cornell.edu/spr/1999-02/msg0014781.html
Re: Gravity: Wave-Particle vs Space-Time Warpage
Subject: Re: Gravity: Wave-Particle vs Space-Time Warpage
From: baez@galaxy.ucr.edu (john baez)
Date: 14 Feb 1999 00:00:00 GMT
Other answers came from a discussion on www.physicsforums.com. Some people
there answered that GR's model of a curved space causing gravity is
totally
at odds with the graviton model of gravity. For instance:
selfAdjoint states:
"The graviton is a theoretical particle predicted by string theory but not
yet demonstrated to exist. If it exists and is the cause of gravity it
will
do away with spacetime curvature and produce gravity the way the photon
carries electromagnetism. Then gravity would be a (quantum) force in your
sense."
"At the present time however, our best theory of gravity is Einstein's
1915
General Theory of Relativity. One of the basic propositions of that theory
is the Principle of Equivalence: On a sufficiantly small scale, it is
impossible to tell the difference between an imposed force and a
gravitational one. Notice that the shape is the shape of spacetime, not
just
of space. Therefore a curved geodesic goes through time as well as space,
and by curving, causes those travelling along it to experience an
acceleration. Anything that produces an acceleration deserves the name
force, no?"
Nenad writes:
"...because if the graviton is found, then there is no curvature of space
time, the reson there is gravity will be because of the graviton. You cant
have both explaining the same thing."
However, some people come to exact opposite conclusion! They hold that the
GR model is compatible with the graviton model of gravity. For instance:
jtolliver writes:
yes, if the graviton is found, General Relativity will be wrong.
"Not really. Any lorentz-invariant interaction that preserves causality
can
be described in terms of particles. GR satisfies those conditions.
Gravitational waves have many properties traditionally associated with
particles (If you pretend spacetime is flat and you add gravitational
forces
to compensate), such as energy-momentum. Using curved space-time(the
technique traditionally used in GR), and using flat space-time with an
additional force that makes it act exactly as though it were curved(this
was
the technique used in classical mechanics, except that that force didn't
quite make it act exactly as curved space-time) are just different ways of
looking at the same thing. The first way is much more convient
mathematically, and the second way doesn't really explain why we have this
additional force. The graviton's only look like particles when we assume
spacetime is flat. If we assume spacetime is curved we see it is really
only
an effect of the curvature of spacetime, even though it looks exactly like
a
particle."
pmb_phy writes:
...It is not the curvature of spacetime that causes gravitational
acceleration. Spacetime curvature causes two particles moving under to
have
a relative acceleration between them, i.e. spacetime curvature causes
tidal
accelerations. But you can have a gravitational force in the absense of
spacetime curvature."
The graviton is a theoretical particle predicted by string theory
but not yet demonstrated to exist.
It doesn't come from string theory. It comes from quantum gravity/quantum
field theory.
If it exists and is the cause of gravity it will do away
with spacetime curvature ...
That is incorrect. The graviton is responsible for producing gravitational
forces, not just tidal forces. Therefore one should aslo be able to detect
gravitons in a gravitational field even when the spacetime is flat. The
graviton, if it exists, will have a relative existance in that sense.
yes, if the graviton is found, General Relativity will be wrong.
if the graviton is found, then there is no curvature of space time,
the reson there is gravity will be because of the graviton. You cant
have both explaining the same thing.
That is very much incorrect. You can most certainly have both. If the
graviton is detected then we will have the mechanism behind GR. Gravitons
are certainly not inconsistent with general relativity.
Couldnt you say the graviton cause the curvature of spacetime...lol
Absolutely. That is 100% correct.
Gravity is not like other forces like the electric of magnetic forces. The
gravitational force is an inertial force where the others aren't.
---
Ok, so which view is correct? (References to peer-reviewed lit, or books
by
respected authors, would also be appreciated.)
Thanks,
Robert
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