Spacetime curvature (1 Viewer)

Users Who Are Viewing This Thread (Users: 0, Guests: 1)

General relativity has it that the spacetime continuum is curved. The physics of continuum is dealt with [stress] tensors.

My questions:
(1) The presence of a mass creates the curvature in spacetime. By how?
(2) If the curvature due to matter is positive, is the curvature due to antimatter negative?
(3) If the gravitational mass of matter is positive, is antimatter gravitational mass negative?
(3) Do other fundamental interactions (the strong, the weak, and electromagnetic) create curvatures in their respective fields?

I am working on the source of gravity, which I cannot reveal due to the Forums rules.
 
27,176
3,812
(1) The presence of a mass creates the curvature in spacetime. By how?
It is not just mass, it is the entire stress-energy tensor. For a brief overview see http://en.wikipedia.org/wiki/Stress-energy_tensor

(2) If the curvature due to matter is positive, is the curvature due to antimatter negative?
No. Antimatter has a positive mass/energy density.

(3) If the gravitational mass of matter is positive, is antimatter gravitational mass negative?
No. See (2).

(3) Do other fundamental interactions (the strong, the weak, and electromagnetic) create curvatures in their respective fields?
Yes. Any energy will curve spacetime see the stress-energy tensor.

I am working on the source of gravity, which I cannot reveal due to the Forums rules.
Thank you for abiding by the rules.
 
(1) Not a pertinent answer. How is the stress tensor created?
I thought the curvatures were in the spaceime continuum (x-y-z-t).

(2) and (3): I agree.

(4) I believe these forces are mediated by exchange of respective bosons. The strong - gluons. The weak: W and Z vector bosons. Electromagnetic - photons. I know the Standard Model well, but I never thought of stress tensors in those fundaamental interactions.
 

Mentz114

Gold Member
5,258
238
(1) Not a pertinent answer.
It is the best answer you'll get because GR does not tell us the 'by how' answer.

How is the stress tensor created?
Not sure what you mean. Did you look at the Wiki article ?
 
27,176
3,812
(1) Not a pertinent answer. How is the stress tensor created?
The same way that energy, momentum, pressure, etc are normally created: By the presence of matter or fields.


I thought the curvatures were in the spaceime continuum (x-y-z-t).
Yes.
 
131
2
(1) Not a pertinent answer. How is the stress tensor created?
I thought the curvatures were in the spaceime continuum (x-y-z-t).

(2) and (3): I agree.

(4) I believe these forces are mediated by exchange of respective bosons. The strong - gluons. The weak: W and Z vector bosons. Electromagnetic - photons. I know the Standard Model well, but I never thought of stress tensors in those fundaamental interactions.
I don't know what you mean by how the stress tensor is created. In my opinion, the stress tensor include all the information we need to create spacetime curvature, such as the energy density, momentum density and pressure.
For SM lagrangian, the stress energy-momentum can be defined as the variation of the action with respect to the metric. Anyway, it's just a semi-classical theory, because we do not quantize the metric field.
 
Sorry, I did not say it right: how is the stress tensor created. I will be responding to you all who kindly answered my questions. I learned from you. Thank you.

Here is the situation. There is a piece of matter with mass in a spacetime continuum. GR has it that the spacetime continuum is a field of space-time geometry and that the mass creates warp/curvature in that field of spacetime geometry. (The spacetime geometry is a complex geometry with x, y, z, ict. So, whatever GR is doing, it is the projection of that on the said complex space.)

A force or a torque creates stress in a deformable continuous medium. The mathematical properties of that stress are represented by stress tensor. (Stress tensor does not create deformations in the medium.)

A force imparts a mass momentum and energy. (Pressure is a form of many momenta, temperature is due to translational motions). Forces are mediated/created. For examples, the strong force is mediated by gluons, the weak by W and Z bosons, and electromagnetic by photons. It is conjectured that gravity is mediated by gravitons. Thus, according to GR and quantum mechanics, gravitons are the quanta of the field of spacetime geometry.

So, I come back to “How a mass creates warp/curvature in the spacetime continuum.” (By the way, the great astrophysicist E. A. Milne asked this question a quarter century ago. We owe him an answer.)

Sooner or later, GR must accommodate Mach’s principle: “The inertial mass of a particle is determined by the gravitational effect of all the other matter in the universe.”

We are physicist first, mathematician second. We must at least try to determine how Nature in a given situation works.

I will bring in the sign of matter or antimatter gravitational mass later, maybe under another topic. This has implications for GR.
 

Mentz114

Gold Member
5,258
238
SinghRP said:
So, I come back to “How a mass creates warp/curvature in the spacetime continuum.”
I repeat, GR does not tell us how this happens. What we have is a set of equations that relate curvature to the SET of the source, Gab=kTab. Or in the case of vacuum solutions, the RHS is zero !

Sooner or later, GR must accommodate Mach’s principle: “The inertial mass of a particle is determined by the gravitational effect of all the other matter in the universe.”
I think you'll find this view is much disputed. I myself regard it as complete hogwash. If we assume the equivalence principal it becomes a tautolgy without meaning.

[ In the words (nearly) of the writer A.A Milne - "A physicists life is terrible hard, says Alice" ]
 
5,600
39
I'm not at all sure a number of statements in post #7 are correct....nor what their point may be...
but I do like: " (By the way, the great astrophysicist E. A. Milne asked this question a quarter century ago. We owe him an answer.)"

Many here will disagree regarding "why" questions in physics....


In post #8, I'd not go so far as does Mentz, but I agree that the equivalence principle seems to supersede Mach's ideas because it leads more directly to concrete insights and predictions.

Singh:
Sooner or later, GR must accommodate Mach’s principle: “The inertial mass of a particle is determined by the gravitational effect of all the other matter in the universe.”
I myself regard it as complete hogwash.
Instead, I'd say that general relativity DOES incorporate those portions of Mach's principle which are quantifiable...or one might say some of his ideas are expressed withinin GR and others are not believed correct....

See here: http://en.wikipedia.org/wiki/Mach's_principle and also note the Lense Thirring effect which IS an example of Mach's ideas within GR. (See the excerpts of Einstein's letter to Mach on this subject....)
 
Last edited:

Mentz114

Gold Member
5,258
238
If express Mach's principle as

“The inertial mass of a particle is determined by the gravitational effect of all the other matter in the universe.”

and combine with

"inertial and gravitational mass are the same thing"
, we get

“The gravitational mass of a particle is determined by the gravitational effect of all the other matter in the universe.”

The problem is the Mach's principle is not clearly stated. In a cosmological solution, the overall curvature is the result of all the matter/energy in the universe, but if this is to affect an individual body's inertia, there would have to be instantaneous effects.
 
So, I come back to “How a mass creates warp/curvature in the spacetime continuum.” (By the way, the great astrophysicist E. A. Milne asked this question a quarter century ago. We owe him an answer.)
I think this is more a philosophical than a science question but just to spend a few words on it.

The question implies that mass (among other things) is a cause of the curvature of spacetime. We do not know if this is true, one of three things could be the case:

- Mass is the cause of spacetime curvature
- Spacetime curvature is the cause of mass
- They are exactly the same thing

Unfortunately, the answers to philosophical questions tend to generate yet even more questions.
 
5,600
39
The question implies that mass (among other things) is a cause of the curvature of spacetime. We do not know if this is true
I was thinking the same thing when posting my last comments.....I do not think there is any experimental evidence to confirm actual curvature of spacetime...??

I think its because other aspects of relativity like, orbtial precession, the fixed speed of light, bending of light by gravity and time dilation as a result of speed and gravitational potential, so far seem to substantiate relativty....so we take curvature to be correct as well....it would indeed be odd to have all that apparently experimentally verified and then find spacetime doesn't curve.....Is that possible???

Wiki says this:
All results are in agreement with general relativity.[55] However, at the current level of accuracy, these observations cannot distinguish between general relativity and other theories in which the equivalence principle is valid.
http://en.wikipedia.org/wiki/Curved_space_time#Gravitational_time_dilation_and_frequency_shift
 
Last edited:

Mentz114

Gold Member
5,258
238
Naty1 said:
I do not think there is any experimental evidence to confirm actual curvature of spacetime
There never can be. How do you measure 'spacetime curvature' ?

(Radioshack is completely out of curvometers. :biggrin: ).
 
Thank you , parrticularly Metzi114, for confirming my line of thinking: "GR does not describe HOW matter creates warp/curvature in the field of space-time geometry."

Regarding gravitational mass of antimatter, GR and Mach's principle, Principle of equivalence (two meanings), etc., I think my statements are humbly compatible with my colleagues'.

I have a request to one of you who can implement my wish. I wish the Forums create a separate section, such as New Approaches or similar, where physicists may put their current line of work without going through peer review. The Forums need to put in a strong disclaimer though. Two criteria for acceptance would be: (1) internal consistency and (2) not contradictory to accepted physical observations. You never know there could be a gem in one of them. (Einstein's papers on the two relativities did not go through peer reviews -- thanks God!) I recall Niels Bohr: "The opposite of a true statement is a false statement. The opposite of profound truth may well be another profound truth."

To Metzi114: I love A.A.Milne's words. Is s/he related to the great E.A. Milne?

Kind regards.
 
27,176
3,812
The spacetime geometry is a complex geometry with x, y, z, ict.
That is one way of doing special relativity that was in fashion several decades ago, but I believe that it is not compatible with GR and so has fallen out of use.

Sooner or later, GR must accommodate Mach’s principle
I agree with Mentz's comments on this above. I have a great distrust of Mach's principle since it is so vaguely stated as to be experimentally meaningless, and it usually leads to absurd discussions about "otherwise empty" universes that have nothing to do with physics in this universe which is the only one that we can test.

We are physicist first, mathematician second. We must at least try to determine how Nature in a given situation works.
It seems to me like you are looking for a "bedtime story" about how gravity works. We have a theory whose experimental predictions agree with all of the observations made to date. That is all that science can do, test a theory's agreement with experiment. In science, all of the rest (beyond the mathematical framework and the experimental data) is just a story that we tell ourselves to make it easier to remember which variables to plug into the equations.
 
27,176
3,812
I do not think there is any experimental evidence to confirm actual curvature of spacetime...??
There never can be. How do you measure 'spacetime curvature' ?
I disagree with these comments. Some of the effects of GR, e.g. time dilation, can occur in an accelerated reference frame in flat spacetime (equivalence principle), but there are many effects that confirm curvature.

1) relative acceleration of inertial observers
2) deflection of light by the sun
3) precession of Mercury
4) redshifting of the CMB
etc.
 

Mentz114

Gold Member
5,258
238
I disagree with these comments. Some of the effects of GR, e.g. time dilation, can occur in an accelerated reference frame in flat spacetime (equivalence principle), but there are many effects that confirm curvature.

1) relative acceleration of inertial observers
2) deflection of light by the sun
3) precession of Mercury
4) redshifting of the CMB
etc.
Obviously, I disgree. You can't measure spacetime curvature any more than you can measure the vector potential of EM or the wave equation in QM.

What we measure is distance and time, and compare those with predictions. We are measuring gravitational effects, not spacetime curvature, which is only a model ( that works rather well).

There are theories that make the same predictions as GR that do not use curvature.

DaleSpam said:
That is all that science can do, test a theory's agreement with experiment. In science, all of the rest (beyond the mathematical framework and the experimental data) is just a story that we tell ourselves to make it easier to remember which variables to plug into the equations.
 
27,176
3,812
You can't measure spacetime curvature any more than you can measure the vector potential of EM or the wave equation in QM.

What we measure is distance and time, and compare those with predictions. We are measuring gravitational effects, not spacetime curvature.
Curvature is simply a deviation of distances and times from what you would expect if the spacetime were flat. If you can measure distance and time then you can measure curvature.

But kudos on very good use of my own words against me :smile:
 
Last edited:

pervect

Staff Emeritus
Science Advisor
Insights Author
9,314
697
We can compute the curvature given that we know the behavior of clocks and rulers. With SI standard clocks and SI standard rulers, one can't avoid concluding that space-time is curved from their observed behavior.

It may be possible to hypothesize a fundamentally flat underlying space-time in which the standard clocks and rulers are deformed / influenced by gravity. Some theorists have done this as an approach to quantum gravity, i.e. http://arxiv.org/abs/gr-qc/9512024. But this requires the introduction of different rulers and clocks than the ones we actually measure things with.

I'm not aware of any popular treatments that take this non-standard approach, though it has some promise as dealing with curvature seems to confuse a lot of people.

It's also unclear if/how this approach would deal with black holes or other situations where global topological issues arise, though it appears to give results equivalent to GR on a small scale.
 

The Physics Forums Way

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving
Top