What is the conflict between General theory of relativity and Quantum theory?

[G.S.RAMYA]

General relativity and Quantum theory are two pillars of physics... The unified theory concept trying to combine 4 basic forces of nature. I don't know what is the actual conflict between gravitational force and other 3 forces?

 

[Mark M]

General relativity and Quantum theory are two pillars of physics... The unified theory concept trying to combine 4 basic forces of nature. I don't know what is the actual conflict between gravitational force and other 3 forces?

Hi,

There are many problems when trying to combine them, I'll explain a few.

First of all, there's the mathematics. When trying to combine the formulas of GR and QM to calculate something, the same answer is always yielded: infinity, which is nonsense.

Next there is the issue of spacetime curvature. In GR, spacetime is continuous and flat like a placid lake. But in QM, the Heisenberg Uncertainty Principle says nothing can have an absolute value. This also includes the gravitational field. Since the gravitational field is determined by the curvature of spacetime, that would mean on small scales, space would not be continuous and smooth, but rather would be violently curved and fluctuating up and down.

Then, there is the problem of quantization. In QM everything can be broken down to basic particles, such as the quark, the photon, the gluon, etc. But in GR, spacetime isn't broken down into discrete packets, like QM claims.

In QM, the universe is non-local, so events can effect each other instantaneously, even if they are light years apart. But GR says, like in classical physics, you must traverse the space in between to have an effect on an event.

Also, in the standard model, particles are zero dimensional. Therefore, the moment and place the collisions between particles, say, and electron and positron, must be agreed on by every observer. But it is an important fact of relativity that certain events can be disagreed on by different frames of reference.

 

[Chalnoth]

In QM, the universe is non-local, so events can effect each other instantaneously, even if they are light years apart. But GR says, like in classical physics, you must traverse the space in between to have an effect on an event.

This isn't true. It's pretty trivial, in fact, to show that it is not possible to transmit information in QM faster than light. The apparent non-local effects are just that: apparent. They are not real.

Anyway, I thought I'd just list two other ways:

1. In quantum mechanics, time and space are a fixed background. The various quantum mechanical particles all interact with one another, but do not impact the behavior of the background. General Relativity describes the interaction between this background space-time and matter. Taking this into effect, then, requires, at the very least, a massive rewriting of quantum mechanics, as it could no longer treat space and time as fixed parameters. Attempts to do this so far have largely failed (though loop quantum gravity and string theory are two candidate attempts).

2. In quantum mechanics, objects can exist in a superposition of states. General Relativity has no sense of superpositions. For example, a hydrogen atom may be in a superposition of the n=0 (ground) state and n=1 (first excited) states. These states have different energy. So if the atom is in a superposition of these two energy states, what is the gravitational field? Trying to put the gravitational field into a similar superposition of states doesn't work, at least not in the simple manner of doing this. So the answer is, at the very least, incredibly non-obvious.

 

[D H]

First of all, there's the mathematics. When trying to combine the formulas of GR and QM to calculate something, the same answer is always yielded: infinity, which is nonsense.

This isn't correct. The problem with the mathematics is that physicists don't know how to combine general relativity and quantum mechanics. There is one place where the mathematics of each can be used to compute the same quantity, the vacuum energy density. General relativity yields a tiny value while quantum mechanics yields a huge value. The two differ by a factor of about 10¹²⁰.

Then, there is the problem of quantization. In QM everything can be broken down to basic particles, such as the quark, the photon, the gluon, etc. But in GR, spacetime isn't broken down into discrete packets, like QM claims.

This, too, is incorrect. Quantum mechanics assumes spacetime is continuous. Spacetime is not quantized in quantum mechanics.

Also, in the standard model, particles are zero dimensional. Therefore, the moment and place the collisions between particles, say, and electron and positron, must be agreed on by every observer. But it is an important fact of relativity that certain events can be disagreed on by different frames of reference.

Also incorrect. Here you are talking about special relativity, not general relativity. Quantum mechanics and special relativity have been merged in quantum electrodynamics.

 

[Chalnoth]

This isn't correct. The problem with the mathematics is that physicists don't know how to combine general relativity and quantum mechanics. There is one place where the mathematics of each can be used to compute the same quantity, the vacuum energy density. General relativity yields a tiny value while quantum mechanics yields a huge value. The two differ by a factor of about 10¹²⁰.

You can't compute the vacuum energy from General Relativity. The vacuum energy is an input parameter in GR, not a computed number.

That said, yes, it is correct that the problem is that the combination of the two is ambiguous (such as the superposition of states situation I mentioned earlier).

This, too, is incorrect. Quantum mechanics assumes spacetime is continuous. Spacetime is not quantized in quantum mechanics.

Though to be fair, it is often thought likely that space-time is quantized in the true theory of quantum gravity (whatever that theory happens to be).

 

[Mark M]

This isn't correct. The problem with the mathematics is that physicists don't know how to combine general relativity and quantum mechanics. There is one place where the mathematics of each can be used to compute the same quantity, the vacuum energy density. General relativity yields a tiny value while quantum mechanics yields a huge value. The two differ by a factor of about 10¹²⁰.

Don't they also disagree on singularities? The equations of GR give infinite density, I thought QM suggested that they can have an actually size, such as the Planck Length.

Also, trying to fit gravitons into general relativity also leads to ultraviolet divergences, without any way of renormalizing(except a theory of quantum gravity, of course.)

For example, trying to use two gravitons in a Feynman diagram leads to infinite, nonsensical answers.

This, too, is incorrect. Quantum mechanics assumes spacetime is continuous. Spacetime is not quantized in quantum mechanics.

Thanks for correcting that, I should have said the gravitational field is continuous in GR, but it is quantized into gravitons in QM.

Though, what I was trying to get at was that fact that at distances shorter than the Planck Length, the idea of smooth space vanishes in favor of violently curved quantum foam.

 

[Nabeshin]

Don't they also disagree on singularities? The equations of GR give infinite density, I thought QM suggested that they can have an actually size, such as the Planck Length.

Well the story goes like this. If you imagine compressing something (a star, the universe) down and down, GR holds just fine, and QM is unimportant. At least, until you get to the Planck length. The Planck length is precisely the dimensionful length you would expect when gravity and quantum effects are both necessary to describe the situation. So in a sense, we can only believe our GR solution down to the point where the object has compressed down to the Planck scale. Beyond that, we obviously need quantum gravity, but as far as what QG will say on the matter, nobody knows (could be there is still a singularity!).

 

[Mark M]

Well the story goes like this. If you imagine compressing something (a star, the universe) down and down, GR holds just fine, and QM is unimportant. At least, until you get to the Planck length. The Planck length is precisely the dimensionful length you would expect when gravity and quantum effects are both necessary to describe the situation. So in a sense, we can only believe our GR solution down to the point where the object has compressed down to the Planck scale. Beyond that, we obviously need quantum gravity, but as far as what QG will say on the matter, nobody knows (could be there is still a singularity!).

Thanks for clarifying that!

Though, what I was trying to say was that standard QM (electromagnetic force, weak nuclear force, and strong nuclear force, no gravity) fails to renormalize GR's infinities in a singularity, because, like you said, at the Planck length gravitons would be required, and standard QM can't handle graviton interactions.

 

[Chalnoth]

So in a sense, we can only believe our GR solution down to the point where the object has compressed down to the Planck scale. Beyond that, we obviously need quantum gravity, but as far as what QG will say on the matter, nobody knows (could be there is still a singularity!).

Well, the Planck length is the length at which we can be very sure that General Relativity breaks down. But I'd be very, very surprised if it didn't break down long before that in reality.

Also, I don't think a singularity is physically possible, as a singularity is nonsensical.

 

[Nabeshin]

Well, the Planck length is the length at which we can be very sure that General Relativity breaks down. But I'd be very, very surprised if it didn't break down long before that in reality.

Also, I don't think a singularity is physically possible, as a singularity is nonsensical.

Of course, you start getting large deviations from GR before the Planck length. How nonsensical these predictions are is impossible to know without an accurate theory of QG, so all we can really say is what you say: At l_p, we're almost positive GR is not a correct description.

With regards to singularities, I agree that such a physical object is nonsense, but that's not what I said. Whatever theory of QG could still predict such a mathematical beast, just as GR did (assuming such a theory of QG is not some kind of 'ultimate theory of everything', but whatever that means is a long tangent). If the cosmic censorship hypothesis is correct, it could be reasonable that a physical description of such objects can never be made concrete, since they are doomed to remain forever within event horizons. On the other hand, of course (and this is more likely IMO), the theory could predict some other as of yet unknown behavior for the objects.

 

[Chronos]

In mathematical terms, a singularity is the value or range of values of a function for which a derivative does not exist. In more common usage a singularity is the point at which our models cease to be predictive. Most scientists view a singularity as a defect in the model as opposed to something tangibly infinite in some respect. One of the great successes of quantum theory was development of renormalization techniques that resolved the infinities that formerly plagued quantum field theory. Unfortunately, we have not figured out how to renormalize gravity.

 

[sahmgeek]

Hi,

There are many problems when trying to combine them, I'll explain a few.

First of all, there's the mathematics. When trying to combine the formulas of GR and QM to calculate something, the same answer is always yielded: infinity, which is nonsense.

This is a point in theoretical physics that really puzzles me. Why assume that the math is wrong when it yields infinity? Just b/c infinity does not occur in nature as we experience it does not make it nonsense as it relates to the TOE. Isn't it likely that by ignoring this conclusion you may be disregarding one of the biggest pieces of the puzzle?

 

[sahmgeek]

Disregarding as accurate that which you can't understand, even after it's been shown to you, is like a dog chasing his tail.

 

[dkotschessaa]

This is a point in theoretical physics that really puzzles me. Why assume that the math is wrong when it yields infinity? Just b/c infinity does not occur in nature as we experience it does not make it nonsense as it relates to the TOE. Isn't it likely that by ignoring this conclusion you may be disregarding one of the biggest pieces of the puzzle?

I know a "guy on the internet" (who is usually a quack but sometimes makes good points) who claims that Cantor proved that "infinity is nonsense" and so dismisses any theory that yields infinities or anything in cosmology described as infinity (such as the idea that the universe might be infinite. A fact physicists usually stop short of saying.)

I am familiar with Cantor's work on infinity, but I'm not sure that this is quite what he was getting at. He proved that there are different types or degrees of infinity, but I don't think this is the same as saying "infinity is nonsense." I'm also not sure of the relevance of his work to physics, though I have heard of "Cantorian space time." (No idea what it is)

Lots of cool stuff to be explored here though I think. I'd be interested to hear what people think.

-Dave K

 

[bapowell]

This is a point in theoretical physics that really puzzles me. Why assume that the math is wrong when it yields infinity? Just b/c infinity does not occur in nature as we experience it does not make it nonsense as it relates to the TOE.

So how should we "perceive" infinite spatial curvatures of the kind that result from metric singularities? If our physical theories no longer align with our perception of reality, then are we doing science?

 

[dkotschessaa]

So how should we "perceive" infinite spatial curvatures of the kind that result from metric singularities? If our physical theories no longer align with our perception of reality, then are we doing science?

Of course. If science was about perception then we'd still be living in a geocentric model on a flat Earth on the backs of turtles (ok maybe not the turtles, I haven't seen them). Don't you think? or did you mean something else?

-DaveK

 

[bapowell]

Of course. If science was about perception then we'd still be living in a geocentric model on a flat Earth on the backs of turtles (ok maybe not the turtles, I haven't seen them). Don't you think? or did you mean something else?

No, I don't. I actually have no idea what you mean.

EDIT: Sorry, that response was curt and unhelpful. What I mean to say is that science uses empiricism to form a representation of reality. You seem to be suggesting that we should suspend this correspondence in the face of mathematical singularities.

 

[sahmgeek]

So how should we "perceive" infinite spatial curvatures of the kind that result from metric singularities? If our physical theories no longer align with our perception of reality, then are we doing science?

we can't "perceive" infinite anything, but we can ponder the concept. you need more than science (though science is a key part) to understand all of this.

 

[bapowell]

we can't "perceive" infinite anything, but we can ponder the concept. you need more than science (though science is a key part) to understand all of this.

So you're suggesting that we use science while it works and then once it doesn't we replace it with something else? Like what?

 

[sahmgeek]

So you're suggesting that we use science while it works and then once it doesn't we replace it with something else? Like what?

i'm not suggesting that we replace it at all. rather, I'm suggesting that it has it's limits. my personal opinion is that a multidisciplinary (science/physics/math, cognition/neuroscience, linguistics, and philosophy) approach may get us closer to an answer. each discipline on it's own has it's limits, but they can certainly be used to inform each other, i think, to gain a broader understanding.

 

[bapowell]

I don't know. It seems more reasonable to me to suggest that a physical theory has a regime of applicability, and that singularities simply exist outside this regime, then to suggest that singularities exist outside the regime of applicability of the whole empirical framework of science. After all, we have specific examples of theories that are relevant only within certain energy ranges.

I interpret your suggestion to be an example of "God of gaps", but rather than religion, you want to apply philosophy and other schools of ostensibly unrelated thought to the problem. I'm going to err on the side of Occam and suggest that we simply continue exploring empirically-verifiable explanations for the natural universe -- there is no evidence or compelling to reason to suspect that they have failed in this case.

 

[Mark M]

i'm not suggesting that we replace it at all. rather, I'm suggesting that it has it's limits. my personal opinion is that a multidisciplinary (science/physics/math, cognition/neuroscience, linguistics, and philosophy) approach may get us closer to an answer. each discipline on it's own has it's limits, but they can certainly be used to inform each other, i think, to gain a broader understanding.

Like bapowell said, just because our current theories don't give us a good answer, doesn't mean science can't.

Take gravity for example - Newton had created extraordinarily accurate laws to describe how mass affects gravity, and how gravity affects matter. But he was baffled as to why gravity occured, or what the mechanism was that caused it.

Then comes along Einstein over 200 years later, discovers general relativity, and completely revolutionizes physics - all done with science. What if scientists figured that since the problem alluded their current theories, there was no answer within science, and just let it be to religion. Then where would physics be today?

The point I'm trying to make is that just because we can't fully understand something right now, doesn't mean we never will and must resort to philosophy and guessing. So, we know there is a better answer than an infinitesimal singularity, we don't just accept it. We finish developing QG, then tackle the problem and get a better answer.

 

[sahmgeek]

I'm going to err on the side of Occam and suggest that we simply continue exploring empirically-verifiable explanations for the natural universe -- there is no evidence or compelling to reason to suspect that they have failed in this case.

I absolutely agree. I just think "science" and scientists should be keenly aware of the underlying assumptions that exist in the language and explanations used to describe empirically verifiable natural phenomena. This is clearly beyond the scope of this thread.

But, i don't think my origin question was answered (at least not to my satisfaction): Why assume that the math is wrong when it yields infinity?

 

[sahmgeek]

So, we know there is a better answer than an infinitesimal singularity, we don't just accept it.

I missed the part relating to how you know this? I have no idea if there is a better answer or not. I was just playing devil's advocate and asking what the implications might if this is the most accurate explanation.

 

[sahmgeek]

also, i don't think a singularity is nonsensical at all (at least not conceptually), especially if space and time turn out to be one and the same.

 

[Mark M]

I missed the part relating to how you know this? I have no idea if there is a better answer or not. I was just playing devil's advocate and asking what the implications might if this is the most accurate explanation.

Because getting infinity as a result of a mathematical equation in physics usually means you went wrong. Simply, infinity is a mathematical concept, not a number - it does not exist in the physical world.

For example, imagine a star undergoing gravitational collapse. Let's say we were somehow able to measure it at every moment in time. As we let time pass, it would continue to shrink - but would always have a definite size. Even if this was incredibly low, I would still be able to give a number describing it's size. Whether it be 1 meter, or 10^-33(the Planck Length) it still is definitely measurable. (Obviously, you would be very challenged to do this without be ripped to shreds by the black hole)

And to put it into a more concrete argument - most quantum theories of gravity (LQG and String Theory included) don't allow for matter to shrink down to an "infinitesimal" size. In the case of String Theory, it is because strings have a definite length, and in LQG it is because space and time are quantized.

Also, in the case of the Big Bang. If the observable universe was of infinitesimal size, then it would take in infinite time to reach and a finite size. Obviously not agreeing with the fact it has a finite size now, because you can't make a jump between infinite and finite.

EDIT: One more situation more pertinent to the original topic:

Because general relativity does not single out any special spacetime, this comes into conflict with quantum field theory, which uses a background-independent Minkowski Space. This difference causes graviton interactions to result in infinite amounts of energy, which is obviously an impossibility.

 

[Whitewolf4869]

Space is nothing. Time is what happens to matter and energy

 

[sahmgeek]

Because getting infinity as a result of a mathematical equation in physics usually means you went wrong. Simply, infinity is a mathematical concept, not a number - it does not exist in the physical world.

certainly, i get that this is perplexing. perhaps that's the point (and it may not be "wrong"). *shrug*

 

[dkotschessaa]

No, I don't. I actually have no idea what you mean.

EDIT: Sorry, that response was curt and unhelpful. What I mean to say is that science uses empiricism to form a representation of reality. You seem to be suggesting that we should suspend this correspondence in the face of mathematical singularities.

I think I took issue with the word "perception." Now you say "empirical" which sounds more like science to me. Of course, I think that if our theories fail to match up with empirical evidence then we need to re-examine the theories.

-DaveK

 

[Chalnoth]

With regards to singularities, I agree that such a physical object is nonsense, but that's not what I said. Whatever theory of QG could still predict such a mathematical beast, just as GR did (assuming such a theory of QG is not some kind of 'ultimate theory of everything', but whatever that means is a long tangent).

Well, yes, it is always possible that we will find a reasonably-accurate theory of quantum gravity that still includes singularities. However, that will just be evidence that theory is an effective theory and not a fully accurate one.

Of course, all scientific theories to date are effective theories. So this wouldn't be a strike against quantum gravity. It would simply mean there is still more to learn about fundamental physics.

 

[Chalnoth]

This is a point in theoretical physics that really puzzles me. Why assume that the math is wrong when it yields infinity? Just b/c infinity does not occur in nature as we experience it does not make it nonsense as it relates to the TOE. Isn't it likely that by ignoring this conclusion you may be disregarding one of the biggest pieces of the puzzle?

No, it's literally nonsense in that if you put actual infinities into your theory, you can prove silly things like 2=3.

The way this is done in practice is you draw a little circle around the infinity and declare, "Here be dragons!" and never let any of your calculations go there. This is sort of like the prescription in ordinary arithmetic against dividing by zero.

The problem with this is that in reality, you can't do this. That is, with horizons you can sort of kinda hide the behavior of singularities, but you can't hide that behavior from the perspective of the object falling into the singularity. It doesn't seem unreasonable to me to assume that reality must be sensible for all observers.

 

[Nabeshin]

Of course, all scientific theories to date are effective theories. So this wouldn't be a strike against quantum gravity. It would simply mean there is still more to learn about fundamental physics.

I tend to take this view, since it ensures that I (and people like me) will always be employed.

 

[Chalnoth]

I tend to take this view, since it ensures that I (and people like me) will always be employed.

Haha, well, it isn't actually an obstacle. Even if we someday discovered the correct, full description of fundamental physics, then that doesn't mean we would come close to understanding all of its consequences. Hawking was arguing some years back that it isn't actually possible to understand all of the consequences of physics due to Goedel's first incompleteness theorem, so that there will always be more to learn.

 

[sahmgeek]

Well, yes, it is always possible that we will find a reasonably-accurate theory of quantum gravity that still includes singularities. However, that will just be evidence that theory is an effective theory and not a fully accurate one.

Of course, all scientific theories to date are effective theories. So this wouldn't be a strike against quantum gravity. It would simply mean there is still more to learn about fundamental physics.

again, linguistic hangups happening here - Why would a singularity make sense physically? Isn't it, by definition, the very absence of physicality/matter? hence, infinite gravity, etc... To assume that it SHOULD make sense physically is what is nonsensical. no?

also, why do singularities need to be absent from "accurate" theories.

 

[sahmgeek]

The problem with this is that in reality, you can't do this. That is, with horizons you can sort of kinda hide the behavior of singularities, but you can't hide that behavior from the perspective of the object falling into the singularity. It doesn't seem unreasonable to me to assume that reality must be sensible for all observers.

what type of object would be able to observe a singularity?

 

[Chalnoth]

what type of object would be able to observe a singularity?

Anything that falls into the singularity.

 

[sahmgeek]

Anything that falls into the singularity.

??

Singularities = infinite density (most likely in the form of energy, not in the form of matter since their is also infinite gravity, right?)

does energy make observations? what I'm getting at is that i don't think an "observer" of any kind that we are familiar with could exist at a singularity. could it?

 

[Mark M]

certainly, i get that this is perplexing. perhaps that's the point (and it may not be "wrong"). *shrug*

Did you read the rest of my post?

Infinity is a mathematical concept, it doesn't make sense to use it in the real world, it is absurd. You can make 2+2=5, or pretty much anything you want using infinity.

Like I said in my previous post, if the center of a black hole was a singularity, then it would have infinite density, implying infinitesimal size. I something is infinitesimal, then it would have taken an infinite amount of time to get that way. Which is obviously impossible.

 

[Chalnoth]

??

Singularities = infinite density (most likely in the form of energy, not in the form of matter since their is also infinite gravity, right?)

does energy make observations? what I'm getting at is that i don't think an "observer" of any kind that we are familiar with could exist at a singularity. could it?

It's always possible to use a hypothetical point particle as an "observer", usually called a test particle. The behavior of all such test particles should be sensible, no matter their path. Claiming anything else would literally be nonsense.