An Apparent Contradiction in General Relativity?

[Juan Largo]

I'm reading a book about unification of general relativity and quantum physics. The author states that one of the axioms of GR is background-independence, meaning that space-time has no external reference points. All distances and motions in space-time are relative. On the other hand, the standard interpretation of gravity according to GR states that two objects fall toward each other because their straight-line geodesics intersect as the objects travel through curved space-time.

Every book I've read about GR gives the same explanation. However, the very notion of traveling along geodesics through curved space-time clearly violates background independence, which is the basis of GR. If all objects are traveling together "through" space-time (being background-independent), then where could they be "traveling" to? What makes them travel? What is their "destination"? Is there another way to interpret gravity within the context of GR without violating background independence?

 

[Dale]

Do you have a reference supporting this claimed contradiction?

I don't see how the notion of traveling along geodesics violates background independence as long as the distribution of matter is what determines the geodesics. However, I also don't see background independence as a foundational principle of GR.

 

[Juan Largo]

Do you have a reference supporting this claimed contradiction?

Why is a reference necessary?

1. If all things travel "through" space-time, there is a preferred direction of motion.

2. Frame independence means there are no preferred directions or locations.

It seem pretty obvious that Statement 1 contradicts Statement 2.

 

[phinds]

Why is a reference necessary?

Because that is how this forum works. If you make a statement, you have to be able to back it up with mainstream science, not your own opinion or your interpretation of what you have read.

 

[UltrafastPED]

Why is a reference necessary?

So that we can look at the source of the claim, and make an independent evaluation.

 

[UltrafastPED]

1. If all things travel "through" space-time, there is a preferred direction of motion.

What if "things" just happen to be traveling in all possible directions?

 

[Nugatory]

Why is a reference necessary?

https://www.physicsforums.com/blog.php?b=2703

1. If all things travel "through" space-time, there is a preferred direction of motion.
2. Frame independence means there are no preferred directions or locations.
It seem pretty obvious that Statement 1 contradicts Statement 2.

It's hard to be really precise with natural language; when people speak of a "preferred direction" they nearly always mean "preferred spatial direction". Time is different from space even in theories such as GR that treat both as directions in a four-dimensional spacetime.

 

[jedishrfu]

Perhaps a better definition of background independence will help:

http://en.wikipedia.org/wiki/Background_independence

I think the OP is thinking that there is no coordinate system when dealing with two bodies alone in space so how can there be a geodesic.

However in this case, an observer could measure the distance between them as one coordinate and use his/her timetime as a second. That would constitute a spacetime coordinate system from which a geodesic could be discerned.

http://en.wikipedia.org/wiki/Geodesics_in_general_relativity

 

[MikeGomez]

If all things travel "through" space-time, there is a preferred direction of motion.

So is this puzzle equivalent to "Why does time flow in one direction?" ?

 

[Juan Largo]

Because that is how this forum works. If you make a statement, you have to be able to back it up with mainstream science, not your own opinion or your interpretation of what you have read.

Good-bye then.

 

[jedishrfu]

Good-bye then.

Please reconsider, many of us have gone through this phase when we comment on threads and see it vanish because we violated some PF rule, or have been chastised when we give some student an answer to a problem when the student shows no effort.

We deal in mainstream science here with the goal of helping students better understand what they are learning. To discuss speculative things or personal theories confuses some students and muddies the water to understanding.

So read some more posts, read the PF rules and then decide if you really want to quit. Compare PF with other forums and you'll see that this is a nice community where discussion in the pursuit of learning is promoted and where you'll will find better quality information on a particular topic.

 

[stevendaryl]

Why is a reference necessary?

1. If all things travel "through" space-time, there is a preferred direction of motion.

2. Frame independence means there are no preferred directions or locations.

It seem pretty obvious that Statement 1 contradicts Statement 2.

It often helps in understanding the geometry of spacetime to look for analogies with something you already understand. A simple analogy for spacetime is a blank piece of paper. An analogy for the path of a particle is a continuous curve drawn on that piece of paper. You put down a pencil at some point $P_0$, and you start drawing, without picking up your pencil (and without crossing itself). Note that such a curve has a preferred direction, which is the direction away from the starting point, $P_0$.

The piece of paper has no preferred direction, but the curve does. The curve also has a notion of "progress". Any point $P$ along the curve can be associated with a real number, $s$ which increases as you get farther and farther away from $P_0$. The simplest choice is to let $s$ be the distance along the curve from $P_0$, but you could use any other real-valued parameter, as long as it keeps increasing as you move along the curve.

Now, once we've parametrized the curve by a progress parameter $s$, we can re-interpret the curve as a point object "traveling" across the page. Travel in this sense just means that you have a real-valued parameter $s$ that is increasing (it's the curve's notion of "time passing"), and you have a position $P(s)$ that changes as a function of $s$. You can also define a notion of the "velocity" of the object. In terms of coordinates, the velocity is the pair $(\frac{dx}{ds}, \frac{dy}{ds})$, where $(x(s), y(s))$ is the coordinates of the curve at parameter $s$.

So you definitely don't need a preferred direction in order to talk about "traveling". All you need is a way to parametrize paths. In GR, the path taken by a massive object can be parametrized by "proper time", which you can think of as the time shown on a clock that is attached to that object.

 

[bhobba]

Frame independence means there are no preferred directions or locations.

That applies only spatially. For time we have the principle of homogeneity which says all instances of time are equivalent - not directions.

And it is what defines an inertial frame - coordinate systems in GR are a lot more general than that.

Thanks
Bill

 

[phinds]

Good-bye then.

I take it you don't plan on a career in science or engineering. If you do, you might want to reconsider, given your attitude.

 

[PeterDonis]

I'm reading a book about unification of general relativity and quantum physics.

Which book? As others have pointed out, it helps to give specific references. It's particularly helpful when it seems likely that you have misinterpreted what you read; see below.

The author states that one of the axioms of GR is background-independence, meaning that space-time has no external reference points.

Can you give a direct quote? The last part of that sentence ("space-time has no external reference points") is not what background independence means, but I can't tell whether that's your misinterpretation or the author's.

Background independence in GR means that the entire spacetime geometry is dynamic, i.e., there is no "fixed background" part of spacetime that is not included in the Einstein Field Equation, which is the dynamical equation linking spacetime geometry to its "source", matter and energy.

All distances and motions in space-time are relative.

This is true, but it's not what "background independence" means. All distances and motions are relative in special relativity too, but SR is not background independent: the geometry of spacetime is fixed in SR, not dynamic.

On the other hand, the standard interpretation of gravity according to GR states that two objects fall toward each other because their straight-line geodesics intersect as the objects travel through curved space-time.

Yes.

the very notion of traveling along geodesics through curved space-time clearly violates background independence

No, it doesn't. See above.

If all objects are traveling together "through" space-time (being background-independent), then where could they be "traveling" to?

To other regions of spacetime. Spacetime is the entire universe in GR; there is nothing "outside" it. But there doesn't have to be to be a place for objects traveling on geodesics to "travel to"; they just keep traveling to other parts of spacetime.

However, all this depends in any case on this "traveling" interpretation, which is just an interpretation and is not a necessary part of the physics. You can describe everything in GR in terms of 4-dimensional spacetime, and all the geodesics within it, just "existing", without anything having to "travel" at all. The "traveling" interpretation is a conceptual crutch we humans use because it makes it easier to link up the physics with our ordinary experience.

What makes them travel?

Nothing. "Traveling" is an interpretation, not physics. See above.

Is there another way to interpret gravity within the context of GR without violating background independence?

The "traveling" interpretation has nothing to do with background independence; you can put the same interpretation on SR, which is not background independent, as I showed above. GR is background independent for the reason I gave above.

 

[atyy]

Can one have exact geodesic motion without violating background independence?

When the backreaction is included, I don't think a small body moves on an exact geodesic. For example, "up to order ε² errors, a point mass m moves on a geodesic" http://arxiv.org/abs/1102.0529 (p144)

 

[pervect]

Good-bye then.

It's probably too late in this individual case, but I'd like to clarify something. Debating the correctness of relativity (or other major scientific theories) is outside the scope of physics forums.

Titles like "an apparent contradiction" in relativity (or whatever) such as in this thread don't tend to get much sympathy, it's presumed that the person is looking for a debate, as opposed to answers.

What we can do is try to explain and teach the theories to those who are interested in how they work - this is different than debating them. If one is interested in debate, there are other forums for such "debates", though I can't say how much luck one will have finding technically qualified people who are interested in debating, especially debating with people who aren't technically qualified. Usually the people who debate are the people who like debating as an art into itself, the technical facts wind up subordinate to the desire to "win the debate". In my experience the quality of such "debates" turns out not to be very high, and it also turns out in the end to not be an especially good way to learn the ins and outs of a highly complex subject like relativity (or whatever is under discussion).

While I personally dislike debate and find it mostly unproductive, the forum guidelines don't prohibit it. They do attempt to minimize the worst sort of debate, "uninformed debate" by requiring that the topic under debate have some reference to the published literature, and that the arguments be of a professional level with references to said literature. That's not necessarily a guarantee that the people who are debating actually know anything, but it helps :)

This is my take on the forum guidelines https://www.physicsforums.com/showthread.php?t=414380, which are ultimately interpreted by the staff here.

 

[PeterDonis]

Can one have exact geodesic motion without violating background independence?

When the backreaction is included, I don't think a small body moves on an exact geodesic.

In other words, you're saying that exact geodesic motion presupposes no back reaction, and no back reaction means background dependence--the spacetime geometry is not allowed to respond to the small body's stress-energy. I think this is true, but I think the answer to it is that GR does not require exact geodesic motion except for a test body, which by hypothesis has no influence on the spacetime geometry. In other words, exact geodesic motion is an idealized limiting case, and GR does not claim it to be anything more than that. The question of how close the actual motion of actual bodies is to exact geodesic motion is left open in GR; it depends on the specific situation.

 

[PeterDonis]

Titles like "an apparent contradiction" in relativity (or whatever) such as in this thread don't tend to get much sympathy

I would add that saying "I read somewhere that...", or words to that effect, followed by something which is clearly a misunderstanding of relativity, without giving a reference, also doesn't tend to get much sympathy. I think a lot of posters who do this aren't "looking for a debate, as opposed to answers"; they just don't realize how much they've misunderstood what they've already read, so they don't understand how much they're going to have to change their conceptual scheme in order to understand how relativity actually works.

Of course, combining this with a title such as you describe only makes it worse.

 

[atyy]

In other words, you're saying that exact geodesic motion presupposes no back reaction, and no back reaction means background dependence--the spacetime geometry is not allowed to respond to the small body's stress-energy. I think this is true, but I think the answer to it is that GR does not require exact geodesic motion except for a test body, which by hypothesis has no influence on the spacetime geometry. In other words, exact geodesic motion is an idealized limiting case, and GR does not claim it to be anything more than that. The question of how close the actual motion of actual bodies is to exact geodesic motion is left open in GR; it depends on the specific situation.

Yes. So there is, I think, in spite of the OP's misunderstanding of what "background independence" means, some part of the OP's question which is in fact a good question, since one does hear:

1) GR is background independent.
2) Test particles travel on geodesics in GR.

If one interprets "test particles" as small bodies, eg. in the usual presentation of the perihelion precession of mercury in the Schwarzschild background, then (1) and (2) are contradictory.

 

[maddog]

Concern over requirement for references

I can see the fallacy in Juan's argument because I can do a coordinate transformation from one coordinates system to another without an absolute system so in either SR or GR there is no discrepancy wrt to motion of bodies.

What I did have is concern over his needing a reference to his claim. If it was his claim why did he need a reference. This is saying you only respond to what is published by authors who have published. No other claims can be made. So if I have an original thought & I posit some notion, I can only speak about it, if it has a reference somewhere by someone who published it. Which means, I myself unpublished can not post some original idea, since I have no reference, correct?

Maddog

 

[atyy]

Even the fallacy that GR = background independence = coordinate independence has good pedigree. As stated in "Gravitation" by Misner, Thorne and Wheeler, p917:

"Mathematics was not sufficiently refined in 1917 to cleave apart the demands for "no prior geometry" and for a geometric, coordinate-independent formulation of physics. Einstein described both demands by a single phrase, "general covariance." The "no prior geometry" demand actually fathered general relativity, but by doing so anonymously, disguised as "general covariance", it also fathered half a century of confusion."

 

[phinds]

What I did have is concern over his needing a reference to his claim. If it was his claim why did he need a reference. This is saying you only respond to what is published by authors who have published. No other claims can be made. So if I have an original thought & I posit some notion, I can only speak about it, if it has a reference somewhere by someone who published it. Which means, I myself unpublished can not post some original idea, since I have no reference, correct?

Maddog

There are good places to publish original theories. This forum is not one of them. That is not its purpose.

If you are developing a theory and have a question about something in it that relates to mainstream physics, this is a good forum to ask about that aspect.

If you want to propose your own theory and ask people if they think it is right and why or why not, this is definitely NOT the forum to do that.

If there is anything about mainstream physics that puzzles you, this is a GREAT place to ask.

 

[russ_watters]

What I did have is concern over his needing a reference to his claim. If it was his claim why did he need a reference. This is saying you only respond to what is published by authors who have published. No other claims can be made. So if I have an original thought & I posit some notion, I can only speak about it, if it has a reference somewhere by someone who published it. Which means, I myself unpublished can not post some original idea, since I have no reference, correct?

Yes, that's correct. I had a history teacher in high school who said it quite explicitly: until you start writing your phd thesis, you aren't allowed to have original thoughts. It may hit you in the gut because smart people don't like hearing such things, but the reality is that until you have mastered what is already known by others, you can't know if your thought is even original, much less know if it is at all useful.

 

[jedishrfu]

Yes, that's correct. I had a history teacher in high school who said it quite explicitly: until you start writing your phd thesis, you aren't allowed to have original thoughts. It may hit you in the gut because smart people don't like hearing such things, but the reality is that until you have mastered what is already known by others, you can't know if your thought is even original, much less know if it is at all useful.

I respectfully disagree with the sentiment on not allowing you to have original thoughts until you're ready for a PhD. Students must try to put things together in their own way and they should expect for a teacher to put them right. Its the discourse that builds the analytical skills students need and to do that they must dare to be original even when they're not.

I've seen this process at work in our Patent Review Board. People come in with original ideas which turn out not to be so original. The Patent review chairman would say: "Well its a good idea but like most good ideas someone thought of it before." It left the future inventor feeling wow I can do this if only I can find something more original and that's when they start to really invent.

 

[PeterDonis]

If it was his claim why did he need a reference.

It wasn't just "his claim". He said he was basing it on something he read. But he didn't say where he read it, or give any direct quotes, and so it was impossible to tell whether the obvious misunderstandings in his OP were his own misunderstandings, or were because of misstatements or misunderstandings on the part of the author of whatever he read. If he had given specifics on where he read it, and direct quotes, it would have been a lot easier to see where he was going wrong.

 

[PeterDonis]

I respectfully disagree with the sentiment on not allowing you to have original thoughts until you're ready for a PhD. Students must try to put things together in their own way and they should expect for a teacher to put them right.

That's exactly what the teacher is doing when he says that you're not allowed to have original thoughts until you're ready for a PhD. He's telling the student that what they *think* are their original thoughts, are thoughts that thousands of others have had before them, so instead of getting all excited because they've had an original thought, they should be thinking: "Ok, if I, a mere high school student, can come up with this, somebody else must have thought of it before; so if it isn't already part of the mainstream stuff I'm getting taught in class, there must be something wrong with it. So I should try to figure out what that something wrong is."

On a more positive note, I would add that even having wrong thoughts on a subject requires a certain amount of understanding; most newbies' thoughts on most subjects are "not even wrong".

Its the discourse that builds the analytical skills students need and to do that they must dare to be original even when they're not.

And then they must take the next step and figure out why the thought they think is original and groundbreaking, is actually not so original, and wrong. One of the best analytical exercises you can do is to figure out what is wrong with an idea you have had yourself; that's much harder than seeing what is wrong with other people's ideas.

 

[Dale]

I have really appreciated hearing how many people seem to "get" the forum purpose and understand why we have and enforce the rules we do.

 

[maddog]

Concern over requirement for references

There are good places to publish original theories. This forum is not one of them. That is not its purpose.
If you are developing a theory and have a question about something in it that relates to mainstream physics, this is a good forum to ask about that aspect.
If you want to propose your own theory and ask people if they think it is right and why or why not, this is definitely NOT the forum to do that.
If there is anything about mainstream physics that puzzles you, this is a GREAT place to ask.

I never said that I wish to propose my own theory. If I was ready for that like, Einstein, I would publish as he did in 1905. I do feel there is value in a conjecture. This is some statement that is to be treated as a hypothesis. It has no proof attached to it. So if I were to make such a statement while not claiming it as fact even though my own, I feel I could propose it based on something else said that might have had me think of it. I would not deliberate for long & then proceed on. I would not expect to immediately have to find citations where this had been thought before (unless it had & not original).

For example, I had a thought (conjecture) that Iterative Function mappings (like Mandelbrot set) could be made on any analytic function over at least a pointwise continuous domain and have no more than a countable number of singularities.

I have no proof for this as I have not yet even taken a graduate course in Complex Analysis. I have since speculated this can be extended to over any Composition Division Algebra {C, H, O} which again I have only read on this subject on my own with no formal study.

Yes, that's correct. I had a history teacher in high school who said it quite explicitly: until you start writing your phd thesis, you aren't allowed to have original thoughts. It may hit you in the gut because smart people don't like hearing such things, but the reality is that until you have mastered what is already known by others, you can't know if your thought is even original, much less know if it is at all useful.

I would have called that high school history teacher a dweeb. I probably would flunk his class too.

I respectfully disagree with the sentiment on not allowing you to have original thoughts until you're ready for a PhD. Students must try to put things together in their own way and they should expect for a teacher to put them right. Its the discourse that builds the analytical skills students need and to do that they must dare to be original even when they're not...

I appreciate the support. Thank You.. I have seen where even mathematicians and the like make a conjecture, only with intention to return later to prove. For me to return, I would need more formal training. Alas, I didn't continue on to graduate school (Physics) even though I started nearly finishing an Astrophysics BS before switching to Physics nor later did I complete a MS in Pure Mathematics.

That's exactly what the teacher is doing when he says that you're not allowed to have original thoughts until you're ready for a PhD. He's telling the student that what they *think* are their original thoughts, are thoughts that thousands of others have had before them, so instead of getting all excited because they've had an original thought, they should be thinking: "Ok, if I, a mere high school student, can come up with this, somebody else must have thought of it before; so if it isn't already part of the mainstream stuff I'm getting taught in class, there must be something wrong with it. So I should try to figure out what that something wrong is."
On a more positive note, I would add that even having wrong thoughts on a subject requires a certain amount of understanding; most newbies' thoughts on most subjects are "not even wrong".
And then they must take the next step and figure out why the thought they think is original and groundbreaking, is actually not so original, and wrong. One of the best analytical exercises you can do is to figure out what is wrong with an idea you have had yourself; that's much harder than seeing what is wrong with other people's ideas.

Wrong again. In 1975 after an Astrophysics lecture, I asked the professor of my class, if the energy of a Quasar could be a galaxy with a Black Hole at its center - could that be enough energy release to create the energy speculated to be emitting from it. He thought that was ludicrous there is no way that a Black Hole could be so massive to swallow up a whole galaxy... Oh yah, in 1975 that was sure not original... Today most galaxies are thought to contain BH at their centers & to be very massive.

My only understanding is if I make a conjecture (if original so be it), I want to be able to state it as it is, empirical as it is & not requiring proof, or corroboration or any nonexistent citation. Now, if someone else or myself, were to find it not original, we it me, I would be compelled to say so, & I would expect any different of anyone else.

Sure I have some ideas, I will refrain from stating them until they are ready for publication (if ever), I won't bother to present then on this forum.

maddog

 

[russ_watters]

I respectfully disagree with the sentiment on not allowing you to have original thoughts until you're ready for a PhD. Students must try to put things together in their own way and they should expect for a teacher to put them right. Its the discourse that builds the analytical skills students need and to do that they must dare to be original even when they're not.

Discussion in a teaching situation is freeform and errors in student thinking are to be expected. That rule was given in the context of paper-writing and test essays. It would have been helpful to the OP and here:

I've seen this process at work in our Patent Review Board. People come in with original ideas which turn out not to be so original. The Patent review chairman would say: "Well its a good idea but like most good ideas someone thought of it before."

Better to say: "Why didn't you do your due diligence and research the prior art before submitting this application and wasting the USPTO's time and the taxpayers' money?"

It left the future inventor feeling wow I can do this if only I can find something more original and that's when they start to really invent.

The USPTO's job is to issue patents for new ideas, not to make aspiring inventors feel good.

 

[PeterDonis]

In 1975 after an Astrophysics lecture, I asked the professor of my class, if the energy of a Quasar could be a galaxy with a Black Hole at its center - could that be enough energy release to create the energy speculated to be emitting from it. He thought that was ludicrous there is no way that a Black Hole could be so massive to swallow up a whole galaxy...

I would certainly agree that the professor was wrong to say that. But note carefully how you phrased your question: you didn't say "I think relativity is wrong because it doesn't agree with my new idea". You asked, in effect, "could my new idea be consistent with relativity?" And the correct answer, even in 1975, would have been "yes, it could". Nothing in GR prohibits the existence of supermassive black holes, or having them at the centers of galaxies, and this was known in 1975. The only difference then was that such black holes were not thought to be as common as we now know them to be.

Oh yah, in 1975 that was sure not original...

It wasn't. Misner, Thorne, and Wheeler was published in 1973, and it talks about supermassive black holes, and makes it perfectly clear that they are consistent with GR, and that they could be at the centers of galaxies, and that objects falling into them could release enormous energies in the process. Who was your Astrophysics professor? How in touch was he with the latest developments in black hole physics at that time? (I'm guessing "not very".)

My only understanding is if I make a conjecture (if original so be it), I want to be able to state it as it is, empirical as it is & not requiring proof, or corroboration or any nonexistent citation.

It makes a big difference how you state it. See my comments above.

 

[jedishrfu]

As a clarification the patent review I was talking about, handled internal patents submitted by employees. It's purpose was to recommend potential candidates for due diligence in the Intellectual Property law department. Inventors would submit a brief description and come to present and defend it. Often we would find some web reference or product that already implemented the idea and squash it. Other times we would recommend it for publish so while we don't want we also don't want to be sued by someone filing it.

The chairman taught us to be very diplomatic but this was lost on some of our members who either invented everything there ever was or never invented anything but were experts in some field. It was a fun review board we got see how an idea that can't be patented could be transformed into one that could be.

 

[atyy]

Suppose someone asks "Apparent nonsense in Newtonian mechanics? : Every force has an equal an opposite reaction. If this is true, then nothing can accelerate." Will he be asked for a reference, or will his understandable confusion be clarified?

 

[jedishrfu]

Please CLOSE this thread, it has veered way off course and the OP hasn't responded sine being rebuked for his lack of references.

 

[phinds]

Suppose someone asks "Apparent nonsense in Newtonian mechanics? : Every force has an equal an opposite reaction. If this is true, then nothing can accelerate." Will he be asked for a reference, or will his understandable confusion be clarified?

If he claims that he read this somewhere then I for one would ask for a reference.