# Why does quantum mechanics not marry with the theroy of relativity

## Main Question or Discussion Point

I often hear it said that quantum mechanics does not marry with the theory of relativity because of the problem of gravity which can change the vectoral properties and throw the system out, but I'm pretty sure there's more to it than this, without becoming too maths heavy if possible can someone suggest why this is? I asked someone else and he said to be honest I've never really looked into it? So I thought I'd try here?

Sorry about the spelling mistake I didn't check the title before I posted

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GR works satisfactory for objects with larger and larger mass. For objects with a small mass, such as an electron, gravity can often be neglected. Quantum Mechanics works satisfactory for objects will a small size, such as an electron. However, HUP doesn't work that good for a truck.

How about for objects with a large mass and a small size? That is when things start to get a bit freaky. Freaky in the sense of results that are just about pointless.

DaveC426913
Gold Member
GR is a field theory - it requires that there is a variable with a distinct value at every point in space (just like in an electric or magnetic field). That means every point; the fabric of space is a continuum.

QM states that, as you measure on a smaller and smaller scale, the uncertainty of position or velocity (or energy) goes up. This means that, for any given point in the GR fabric of space, you can have an arbitrarily large amount of energy - even infinite.

So, if you try to plug one formula into the other, you get infinites popping out.

(Figuring this out and being able to verbalize it succinctly has taken years, and I consider it a personal success. In fact, the last piece (that first paragraph) only just fell into place at lunchtime today, while reading 'The Trouble with Physics')

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nrqed
Homework Helper
Gold Member
GR is a field theory - it requires that there is a variable with a distinct value at every point in space (just like in an electric or magnetic field). That means every point; the fabric of space is a continuum.

QM states that, as you measure on a smaller and smaller scale, the uncertainty of position or velocity (or energy) goes up. This means that, for any given point in the GR fabric of space, you can have an arbitrarily large amount of energy - even infinite.

So, if you try to plug one formula into the other, you get infinites popping out.

(Figuring this out and being able to verbalize it succinctly has taken years, and I consider it a personal success. In fact, the last piece (that first paragraph) only just fell into place at lunchtime today, while reading 'The Trouble with Physics')
But all the same comments could be made about the electromagnetic fields. And indeed, there are infinities popping up all over the place while quantizing electromagnetism (which occur because on finer and finer scales, the fields become infinitely "rough" i.e. the two-point correlator of fields goes to infinity). And yet, E&M is a renormalizable theory wit spectacular successes (for example the anomalous magnetic moment of the electron). So the appearance of infinities in itself is not the culprit. It's that in the case of GR, those infinities cannot be "tamed" (the theory is not renormalizable). This is harder to explain in a simple way.

wm
QM incompatible with theory of relativity?

I often here it said that quantum mechanics does not marry with the theory of relativity because of the problem of gravity which can change the vectoral properties and throw the system out, but I'm pretty sure there's more to it than this, without becoming too maths heavy if possible can someone suggest why this is? I asked someone else and he said to be honest I've never really looked into it? So I thought I'd try here?

Sorry about the spelling mistake I didn't check the title before I posted
Two suggestions re your good question:

1. Ask the admin people to fix the title so that later searches of the archive (eg, re ''theory of relativity'') will yield your post and its thread.

2. As you seem to be seeking a simple answer, why not simplify your question by removing ''gravity'' from it? That might help replies re the ''more-to-it-than-gravity'' emerge early in the thread.

Regards, wm

DaveC426913
Gold Member
But all the same comments could be made about the electromagnetic fields. And indeed, there are infinities popping up all over the place while quantizing electromagnetism (which occur because on finer and finer scales, the fields become infinitely "rough" i.e. the two-point correlator of fields goes to infinity). And yet, E&M is a renormalizable theory wit spectacular successes (for example the anomalous magnetic moment of the electron). So the appearance of infinities in itself is not the culprit. It's that in the case of GR, those infinities cannot be "tamed" (the theory is not renormalizable). This is harder to explain in a simple way.
Don't you wreck my dreams!

lol. If only someone here understood the correct reason well enough to explain it simply.

You can use maths if you like but keep it calculus, I'm not au fait with field theories very complex mathematics. Einsteins equations and a little of the Dirac equation probably wouldn't be too taxing, so long as your prepared to explain what it means I'd have no problem understanding it, like the Hermetian is the energy of mass x in a field, or whatever.

Can a mentor correct the spelling mistake: no rush.

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cristo
Staff Emeritus
like the Hermetian is the energy...
I think you probably mean the "Hamiltonian"

I think you probably mean the "Hamiltonian"
I think you might be right.

Is it more of a mathematical incompatibility, or a conceptual one, or both?

DaveC426913
Gold Member
lol. If only someone here understood the correct reason well enough to explain it simply.
Actually, I believe I did do just that. You can't have an explanation QM and/or GR that is BOTH simple AND completely accurate.

SD, I'm sure that you were referring to GR even though you didn't specify it. In most physics circles, if you ask a question like that without specifying either GR or SR you would be laughed at because quantum field theory does marry with SR in a most agreeable way.
Now as for GR, I thought that it was because the particles that are affected by the forces in the Standard Model oscillate at freqencies to high to be affected by gravity. This may als be incorrect as I have very little physics background and am still learning. I would like for someone to explain to me why I might be wrong instead of simply pointing out my mistake.

SD, I'm sure that you were referring to GR even though you didn't specify it. In most physics circles, if you ask a question like that without specifying either GR or SR you would be laughed at because quantum field theory does marry with SR in a most agreeable way.
Now as for GR, I thought that it was because the particles that are affected by the forces in the Standard Model oscillate at freqencies to high to be affected by gravity. This may als be incorrect as I have very little physics background and am still learning. I would like for someone to explain to me why I might be wrong instead of simply pointing out my mistake.
I certainly was, thanks for clarifying though anyway.

Well I have had most of my questions answered, so feel free to get as mathematical and technical as you like - well unless you're answering baryon's questions - this semi laymen is clear on why they don't marry. Seems like they've chosen to live together in uncomfortable agreement and on speaking terms and for the sake of their kids, oh no wait just kidding.

Big up to all the concise and capable people who have supplied very simple but very enlightening responses

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Actually, I believe I did do just that. You can't have an explanation QM and/or GR that is BOTH simple AND completely accurate.
I disagree on both counts. I believe nrqed demonstrated your explanation was plain wrong, it fails to capture the core issue. (I wonder if the real one has anything to do with gravitational charge being inertial mass, since that's what first sets gravity apart from other forces. At any rate, it clearly isn't anything in common with the usual other field theories.)

In my experience, given sufficient understanding of a field of knowledge, pretty much any specific question can be answered simply (though perhaps it also takes some skill to separating all the factors/details that aren't relevent and in stating what's left in a manner non-experts can relate to). Of course, I don't think it's just that I've only understood things that turned out to have been simple. Anyway, it's certainly worth trying to boil one's understanding down to a few lines, since it makes it so much more practical for someone else to spot any flaw.

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DaveC426913
Gold Member
It's that in the case of GR, those infinities cannot be "tamed" (the theory is not renormalizable).
nrqed demonstrated your explanation was plain wrong
So add to my explanation: "and since GR is not renormalizable, those infinities give nonsensical results".

I think you're bifurcating bunnies as far as the OP's question is concerned.

In my experience, given sufficient understanding of a field of knowledge, pretty much any specific question can be answered simply (though perhaps it also takes some skill to separating all the factors/details that aren't relevent and in stating what's left in a manner non-experts can relate to).
Easy to say. I'm fishin' - you're cuttin' bait while telling me I can't fish.

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So add to my explanation: "and since GR is not renormalizable, those infinities give nonsensical results".

I think you're bifurcating bunnies as far as the OP's question is concerned.
With apologies then to the OP, can someone then try to explain simply why GR is not renormalisable?

DaveC426913
Gold Member
The book I'm reading 'The Trouble with Physics' has this to say:

"...gravitational waves interact with each other. They interact with anything that has energy, and they themselves have energy. This problem does NOT occur with EM waves because, though photons interact with electric and magnetic charges, they are not themselves charged, they go right through one another... The problem with quantizing GR is that we didn't take background independence seriously. [Gravitons] are not moving on a fixed background, they change the background."

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I suppose that Quantum Mechanic not marry with the theory of relativity because our colleagues choose a wrong way. They want to find Quantum Mechanic with the helpful of Quantum Gravity. But Quantum Gravity is not a right way, I think. Absolutely sense for me that the right way is Classical General Relativity with gravitational pilot-waves influences to classical test particles. In other words QUANTUM PARTICLES=CLASSICAL TEST PARTICLES+GUIDING GRAVITY WAVES. Than Psi function have the sense of anzac Space-Time Geometry. You can find here http://xxx.lanl.gov/abs/quant-ph/0212139

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The book I'm reading 'The Trouble with Physics' has this to say:

"...gravitational waves interact with each other. They interact with anything that has energy, and they themselves have energy. This problem does NOT occur with EM waves because, though photons interact with electric and magnetic charges, they are not themselves charged, they go right through one another... The problem with quantizing GR is that we didn't take background independence seriously. [Gravitons] are not moving on a fixed background, they change the background."
If you take the background as an infinite field of infinite center-points infinitely spaced, then it is independent of any extent of material, space, time, and movement.

Then you have location and point, without having to have extent. Then again, however, how does one derive any extent from an infinite background, in order to get it to arise without collapsing before it does?

nrqed