Can a field disturb the geometry of a space?

[AlbertEinstein]

hI guys. Back after a vey long time.
The question is-"Consider a 3-d surface on which normal Euclidean geometry is valid. Now assume that electromagnetic field is allowed to pervade the whole of the surface . Now what is the possibility that the geometry of the space will be non-euclidean, if the field is assumed to be quantized ?"

The answer being-"Consider a space with n dimension, and which is pervaded by quantized electromagnetic field. Now, initially, the space is assumed to be euclidean, so its curvature is zero. In this flat background space, the quantized electromagnetic field will behave as if normal classical field where the photons will travel in normal field line trajectories. Since the field lines are present, which geometrically speaking are normally parabolic in the vicinity of a charge, the metric of the space will then be defined by the field lines only. Since every point on the field line is a photon which in turn is occupying a point in space. This makes the space non-euclidean, since there cannot be defined any straight line on this space and surely in euclidean space straight lines do exist. "

Now, is the solution correct ? If it is not correct, then why? and else why?
If the solution is correct, what I feel it difficult to comprehend that an EM field can distort the geometry of a space. Plz someone explain it.

 

[Crosson]

Now what is the possibility that the geometry of the space will be non-euclidean, if the field is assumed to be quantized ?"

The short answer is yes; GR says that the presence of energy (relative to you) causes space to be non-euclidean (relative to you).

Your post contains mostly misconceptions; field lines are not real, and you are using "quantized field in an unusual way.

 

[AlbertEinstein]

this means that the presence of a gravitational field will also distort the geometry. and I didn't understand the last line--"and you are using "quantized field in an unusual way." Is the assumption that the field is quantized imply any condition in the answer?
Also does the geometry the property of n-dimensional space? or does it depend on the energy pervading through it ?

 

[mjsd]

Einstein equation:
$$\displaymath{G^{\mu\nu}=8\pi T^{\mu\nu}}$$where $$G^{\mu\nu}$$ is the tensor representing curvature, $$T^{\mu\nu}$$ the tensor representing energy/momentum. So if you believe in Einstein then presence of energy (like Crosson said) implies non-zero curvature...quantization haven't even entered.

 

[AlbertEinstein]

Ok..

"Since every point on the field line is a photon which in turn is occupying a point in space. This makes the space non-euclidean, since there cannot be defined any straight line on this space and surely in euclidean space straight lines do exist."

But I can take any two points in the space and join it by a staight line? Is this contradictory?please xplain.

 

[MeJennifer]

The short answer is yes; GR says that the presence of energy (relative to you) causes space to be non-euclidean (relative to you).

Well that is an interesting statement. Why do you write relative to you? If the Riemann curvature tensor is curved it must be curved for all observers.

 

[Chris Hillman]

A question which DMS?

Hi, "AlbertEinstein",

Your PF handle could be awkward, since you are presumably not Albert Einstein (1879-1955)!

I agree with Crosson that your post seems to reflect numerous misconceptions and/or incorrect hidden assumptions.

1. One thing which you might clarify is whether you are asking about a question and "answer" you came up with yourself, or whether you are referring to a dialog (with "Niels Bohr"?) in some other forum (would that be afterlife.org or oblivion.com?)

2. In either case, a second thing you should think about is what theory you are asking about when you ask whether the suggested "answer" of your "question" is correct. In this board (see the name!), the "default theory of gravitation" is gtr.

3. Assuming you are asking for how gtr would answer your "question", a third thing you should consider is whether this putative "question" actually makes sense in the context of gtr. That is, you appear to propose a scenario, but you should ask: is this scenario possible in gtr? If not, you can't demand an answer from gtr; that would be like asking your arithmetic teacher: "suppose that one plus one equalled three, then would two times five equal seventeen?" (the problem is that one plus one doesn't equal three, so the question is mathematically meaningless).

 

[AlbertEinstein]

Yeah I may not be Albert einstein but he is my role model. And i don't think that asking such (silly) questions will tarnish him.

the quetion was indeed asked in an another forum (ww.orkut.com). and i answered the question asssuming the Presence of gravitational field. I was unsure if the presence of em field could act in the same way. Finally i was unsatisfied with the answer and therefore posted here to remove my doubts.

in the second case, I too was unsure whr to post the question. If it's in the wrong forum then i hav no objection to move it.

guys , u keep teling tht my post has numerous misconceptions and/or incorrect hidden assumptions. but please tell me wht and whr r they?

thanks.

 

[Chris Hillman]

A nonresponsive response?

Hi, "AE",

I think you took what I wrote the wrong way. I wasn't trying to jerk your chain, I was trying to get you to reread your original post. In the so-called "Socratic method" pioneered by (naturally!) Socrates, the teacher responds to the student's question by suggesting another question, with the intent of inducing you to discover for yourself how you can modify your original question and answer so that they make more sense. See http://en.wikipedia.org/wiki/Socrates#Socratic_method

 

[AlbertEinstein]

No Chris. I wasn't offended. I'm really thankful to u to hear my questions and reply to them. I tried to find some hidden mistakes but really couldn't find it. I shally be very grateful if u could point out the errors and I may then find the solution.
thanks.

 

[Chris Hillman]

Start with your first paragraph in the original post in this thread. Before jumping into quantum gravity, you should discuss a classical gravitation theory, because there currently existst no true quantum theory of gravity, and to use Steve Carlip's phrase, "we can't have a meaningful discussion in a theoretical vacuum". (Carlip is a mathematical physicist at U.C. Davis who works on quantum gravity.) With the substitution of "gtr" for "quantized gravity", you need to clarify what scenario you have in mind, and depending upon what you have in mind, it could well be that your scenario is not compatible with gtr, in which case you would have to specify an alternative theory, or else alter your scenario.

(This is just the first of many apparent hidden assumptions which were not explained and are probably invalid, and in addition I spotted various misconceptions, but depending upon how you react to what I suggested above, the other problems would be moot and I don't think much would be gained from trying to explain them. Rather, as you continue to learn you should steadily acquire enough background knowledge to avoid making similar mistakes in the future.)

 

[AlbertEinstein]

But i haven't mentioned about gtr in my first paragraph? It's "electromagnetic field".

 

[pervect]

My $.02 to Albert Einstein. Don't use words when you don't know what they mean. Doing otherwise gives the impression of a "snow job" at best, of being "not even wrong" at the worst.

Examples: "quantized field" - there's nothign quantum about your question. Unless one deletes all references to "quantized this" or "quantized that", your post just doesn't make sense.

Simillarly, "field line trajectories" doesn't make any sense. "Field lines" could make sense on its own.

Since the field lines are present, which geometrically speaking are normally parabolic in the vicinity of a charge, the metric of the space will then be defined by the field lines only.

I can't even guess what this might be supposed to mean.