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I've heard that if one of these theories is correct then the other must be wrong. What exactly is the conflict between these two theories?

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- Thread starter einsteinian77
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LURCH

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As a general rule, this is not a place for "quick" answers, it usually takes a day or two to get a response. Please do not feel as though your topic is being ignored, that's just the pace of things around here.

The basic conflict between GR and QM as I understand it is as follows. GR presents an image of space-time as being curved, and QM uses probability equations to determine things like location, momentum, etc. Unfortunately, my understanding of these two field is limited by my lack of mathematical education. Therefore, the following paragraph is somewhat speculative in nature.

Because QM deals mainly in probability, the mathematics utilized must bear a strong resemblance to statistical analysis. I do know that in this field, parameters must first be set. So, when attempting to equate the location of an electron (for example), one would tend to keep one's search within a certain general location, which is then narrowed down (probably through a perturbative process). But all of these probabilities exist within a very small area of space, which led to the conflict in the next paragraph (which is not speculative).

As Quantum physicists generally deal with phenomena that take place on a scale much smaller than a molecule, the amount that space is curved over this distance is negligible. Being negligible, it tends to get neglected. But under extreme circumstances, such as those found near the center of a black hole, the curvature of space over these short distances is significant. So far, all attempts to include the curvature of space (and the equations of GR) into the probability equations of QM result in infinite numbers. IOW, if you conduct in mathematical search which allows for the fact that the space in which you are searching is curved, you'll find that, for any potential location you investigate, your electron's probability of being in that exact location is infinite.

Now, as I said before I am no math wiz, but I do know that a probability equation that yields a probability of "p>100%" is incorrect. And one that yields an infinite probability is right out. So, the equations of QM only work for flat space, and GR insists that space is not flat.

The basic conflict between GR and QM as I understand it is as follows. GR presents an image of space-time as being curved, and QM uses probability equations to determine things like location, momentum, etc. Unfortunately, my understanding of these two field is limited by my lack of mathematical education. Therefore, the following paragraph is somewhat speculative in nature.

Because QM deals mainly in probability, the mathematics utilized must bear a strong resemblance to statistical analysis. I do know that in this field, parameters must first be set. So, when attempting to equate the location of an electron (for example), one would tend to keep one's search within a certain general location, which is then narrowed down (probably through a perturbative process). But all of these probabilities exist within a very small area of space, which led to the conflict in the next paragraph (which is not speculative).

As Quantum physicists generally deal with phenomena that take place on a scale much smaller than a molecule, the amount that space is curved over this distance is negligible. Being negligible, it tends to get neglected. But under extreme circumstances, such as those found near the center of a black hole, the curvature of space over these short distances is significant. So far, all attempts to include the curvature of space (and the equations of GR) into the probability equations of QM result in infinite numbers. IOW, if you conduct in mathematical search which allows for the fact that the space in which you are searching is curved, you'll find that, for any potential location you investigate, your electron's probability of being in that exact location is infinite.

Now, as I said before I am no math wiz, but I do know that a probability equation that yields a probability of "p>100%" is incorrect. And one that yields an infinite probability is right out. So, the equations of QM only work for flat space, and GR insists that space is not flat.

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DrChinese

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There is a mystery as to why the two theories are so different, with the hope that one day they will both be shown to be a subset of a greater "theory of everything".

Some exotic experiments are currently being performed which may shed some light on the situation. For instance, is the force of gravity a constant? Do gravity waves really exist? And so on. Current results leave room for interpretation. But we may see some major breakthroughs in coming years.

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Hurkyl

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Now, as I said before I am no math wiz, but I do know that a probability equation that yields a probability of "p>100%" is incorrect.

Well.....

Actually, in my understanding of QM, it is not required that one work with normalized probability distribution functions (pdf); i.e. it doesn't have to add up to 100%. The probabilities are actually relative probabilities, so if f(1) = 2 and f(2) = 6, then the odds of the particle being at point 2 are three times as much as it being at point 1.

For many pdf's, you can divide by the overall total to get a "real" pdf that has the property that it adds up to 100%, but some of them cannot, such as plane wave states.

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LURCH

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Originally posted by Hurkyl

Well.....

Actually, in my understanding of QM, it is not required that one work with normalized probability distribution functions (pdf); i.e. it doesn't have to add up to 100%. The probabilities are actually relative probabilities, so if f(1) = 2 and f(2) = 6, then the odds of the particle being at point 2 are three times as much as it being at point 1.

For many pdf's, you can divide by the overall total to get a "real" pdf that has the property that it adds up to 100%, but some of them cannot, such as plane wave states.

And these total up to values greater than 100%? If f(1) is infinite and so is f(2), then you've done something wrong, yes?

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ahrkron

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Originally posted by einsteinian77

A couple differences I can point out:

1. In GR, there is no objection against simultaneously specifying the location and momentum of particles (or anything), while the structure of QM forbids that. This implies that in GR you can have point-like singularities (including the very initial one, from which the BB started), while QM says such things cannot exist.

2. QM (and QFT and even String Theory) are based on the assumption that spacetime has a flat (Minkowskian) metric, while GR allows for different spacetime configurations. Curved spacetime has not been accomodated on the framework of QM.

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Hurkyl

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And these total up to values greater than 100%? If f(1) is infinite and so is f(2), then you've done something wrong, yes?

Not necessarily something

For example, in calculus, if you're trying to compute a limit and you plug in values and get &infin / &infin, that doesn't mean you did something

Same thing here; if you get infinites, that would mean that you need to try and apply some other snazzy technique to get the real answer. (I believe "renormalization" is related to this)

The problem with gravity & QM, though, is that no technique has been found that gets rid of the infinities (I'm not sure if it has been proven that it cannot be done, though).

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ahrkron

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Originally posted by Hurkyl

Same thing here; if you get infinites, that would mean that you need to try and apply some other snazzy technique to get the real answer.

Yes. I just wanted to comment that there are some cases in which the infinities cannot be removed by selecting a different technique.

(I believe "renormalization" is related to this)

It is, although probability is not the infinite quantity. It can be, for instance, a mass, or a coupling constant. What has to be done (and it does work) is measuring one value for the infinite parameter, and make things so that such infinity is "renormalized" to become the measured number. Then, when you use the renormalized model to compute the value of the same parameter on different conditions (different interaction energy, for example), you do get a number, which can be compared to new experimental data.

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marcus

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Originally posted by einsteinian77

First, here is some physics folklore. To make it easy to talk about, assume planck scale units (c = G = hbar =1)

Imagine an uncharged nonrotating black hole with mass M = 1.

the radius of such a black hole is always 2M, so in this case the radius is is 2 length units.

The Compton wavelength of a particle with mass M is 1/M, so it is 1 length unit.

The Compton describes how quantum mechanically spread out a particle is---how difficult it is to localize.

To localize a particle within 1/M requires expenditure of energy M (heisenb. uncert. princ.) and that much energy would be enough to create another similar particle!

So in the case of our black hole GR says it is a very precisely shaped geometrical structure with radius exaclty 2. But QM says it cannot even be localized that well. Its very location is fuzzy by 1 length unit.

**************************

this is not the real reason that it is challenging to reconcile and unify QM and GR. It is more of a little parable, or even a joke.

But there is GREAT interest in unifying QM and GR, these days, into a quantum theory of gravity.

The research is always done at planck scale because those are the natural units to work with in dealing with basic things and because some of the problems that must be faced appear at this scale.

***************************

Notice that in the story if the black hole were more massive like M=1 million = 10

then the compton would be a MILLIONTH and would not give

any problems. The radius 2M would be 2,000,000 and the uncertainty in position would be a millionth which is very small

compared with the size of the hole and good enough for government work.

For masses much larger than planck mass, the quantum fuzziness does not bother the theory of gravity----all is well.

For masses much smaller than planck mass, like a proton which is on the order of a quintillionth of planck mass, the theory of gravity is kept out of the picture and quantum theory reigns.

the high-energy-particle people say keep GR far from our door and we will not imagine any black holes! We will neglect gravity

and that will be fine because it is very weak compared with our particle forces.

So the planck mass (22 micrograms) is a kind of vague no-mans land border between two jurisdictions----and a place where the two jurisdictions can sometimes come into conflict.

***************

this too is only a story. Instead of fables, why not go

directly to a key player and get it from the horses mouth:

Lee Smolin is a major figure in quantum gravity.

The greatest recent paper on the unification of QM and GR is by

Lee Smolin and is online and is called

"How far are we from the quantum theory of gravity"

March 19,2003 and recently reviewed by John Baez in his

weekly theoretical physics column

The Smolin paper is

arXiv:hep-th/0303185

but it is 90 pages and you are guaranteed to understand only

a few paragraphs, such is life :-(

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marcus

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There is another link to Smolin's paper

It is not a question of "if one theory is correct then the other fails"

Both theories are almost certainly wrong, or rather, they are only

approximations which are good at certain scales but do not work if applied at an inappropriate context.

The aim is to have a quantum theory of gravity which reproduces GR in the limit for large objects and low particle energies

and is in harmony with quantum mechanical principles that have worked so well in the microscopic and high energy arena

and so to reconcile the two by somehow improving both.

GR is merely our theory of gravity. That is all the curved spacetime stuff is, really, just a model of how gravity works.

But it depends on having space be bendable and dynamic, stretchy. This is totally foreign to QM which is built like a brick

house on a determinedly rectangular foundation. The space

on which QM is built is rigid and not dynamic. So our model of

gravity is different from our models of all the other forces.

This difference is at the root of why it is so difficult to reconcile the two.

this too is not my own view but folklore or gleaned from Smolin.

Just giving you my take on it. Not authoritative, just sharing my

personal opinion and perspective. Good luck. the whole field is

very hard

- #13

damgo

In QFT this manifests itself as gravity being non-renormalizable (can't get rid of the infinities)...

- #14

Alexander

Originally posted by marcus

First, here is some physics folklore. To make it easy to talk about, assume planck scale units (c = G = hbar =1)

Imagine an unchargednonrotatingblack hole with mass M = 1.

You must be joking. You can't neglect spin of elementary BH because graviton has a spin (=2, I believe).

That is why your futher conclusions are wrong.

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I've read alot of books on general relativity and Im pretty sure i know what the theory is offering. However, Im not exactly an advanced mathematician so can't understand stand all of it completely. What im curious about is how matter actually "bends" space-time or in other words what is it that matter is doing that bends space-time?

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Tom Mattson

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Originally posted by Alexander

You must be joking. You can't neglect spin of elementary BH because graviton has a spin (=2, I believe).

That is why your futher conclusions are wrong.

No, he is not joking. He is talking about nonrotation in the

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LURCH

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Originally posted by einsteinian77

I've read alot of books on general relativity and Im pretty sure i know what the theory is offering. However, Im not exactly an advanced mathematician so can't understand stand all of it completely. What im curious about is how matter actually "bends" space-time or in other words what is it that matter is doing that bends space-time?

Nobody really knows. QM sometimes suggests that the "curvature" is really the probability curve or potentiality curve (or some such) of a force-carrying partical called a Graviton. So far, this partical remains undiscovered.

I have my own crackpot theory, but that's over in the "...favorite pet theory..." thread (in this same Forum).

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Tom Mattson

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Why not post it in the Theory Development section here at PF?

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Tom Mattson

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marcus

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those two suggestions are excellent, namely

publishing in physicsforums T.D. department and/or

sending to arXiv.

As far as I can see, physicsforum is the best of its sort

and it archives its posts. so if you present a theory in T.D.

and later it is discovered by someone else you can refer

to a specific post and the recorded date on that post---

the date you last edited or revised it.

Everything is email these days so having something in an

electronic archive is the best possible.

Of course you could also print your theories out on paper

and mail them to the Library of Congress or mail them to

yourself and keep the unopened package with the datemark

in your closet . But seriously, what is wrong with archiving

your idea at physicsforums?

If I had an offbeat theory I believe that is what I would do with it, in fact. Life is short and other types of publication are a hassle.

But of course you must do as you please.

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marcus

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Originally posted by einsteinian77

ANY form of energy bends space-time

the key term in the equation determining curvature is an energy density

In today's physics parlance photons do not have mass (mass is equated with inertia of a body at rest) and so there are massless terms which contribute to the energy density that curves space.

Your question is extremely interesting---very basic question and a good one to be asking. I have no idea how the energy density in a region of space manages to bend things, can only congratulate you for asking an intelligent question.

Here are a couple of equation you might look at----the Friedmann equations---derived from the Einstein equation under the

simplifying assumptions of uniformity proposed by Friedmann in 1922. I shall state them in the case where the spatial curvature term k = 0, the now generally accepted case:

a

(a

*a* is the universe's distance scale, used in defining the metric

It is normalized so that it is equal to one at the present time.

the LHS of the second equation is the square of the Hubble parameter by definition.

The second equation has to do with expansion.

a

If you are interested in curvature then you might look at the first equation, since the LHS is in effect a curvature (second derivative) term.

The curvature is seen to depend on the energy density ( rho = energy per unit volume) and the pressure. In the universe at large the pressure produced by matter is very low and not important but in certain special cases (cores of stars) it can be very important and contribute significantly to gravity.

The pressure of dark energy (if it exists) plays a significant role in curving space-time. The special feature of dark energy is that its pressure is equal to minus its density.

To a first approximation, looking at the large scale, this is what causes the curvature:

rho = rho

p = - rho

a

But this does not describe a mechanism! It only shows how the energy density of matter (including a small contribution from radiation) and of dark energy enter into the equation.

I apologize for discussing only the very large scale picture. I am sure you want to think about smaller scale gravity too, where the einstein equations

G

apply without Friedmann's simplifying assumptions. I tend to omit writing c, and newton's G, in this equation, as people often do these days, but if you want you could insert G/c

This G/c

c

Putting that back into the Einstein equation ("putting back the cees and Gees") one has

G

So you see it is this huge force which connects the curvature terms (G

Good luck with figuring out the mechanism! I believe no mechanism is known at present---anyway havent heard of one!

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Alexander

Originally posted by einsteinian77

Send it to any respectable peer-reviewed journal. If the theory is good, it will be published. As to recognition, don't bet much on this horse - I do not know anyone who became wealthy from theoretical physics (if not to count a couple of nobelists in their 60+).

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chroot

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LOL, I can't wait hear einsteinian77's theory... *rubs hands expectantly*

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