One of the simple - although not quite new - consequences of the "swampland" line of reasoning is that pure theories of quantum gravity cannot work.
This conclusion that we will justify below applies to various loop quantum gravities, spin foams, causal and acausal, dynamical and non-dynamical triangulations, tetrahedronizations, and any other misinterpretations of quantum gravity that you have heard of.
Quantum gravity cannot be studied separately from the other forces, and the other forces cannot be thought of as small corrections to quantum gravity.
On the contrary. In every consistent theory (and background) of quantum gravity,
- gravity must be the weakest force (much like in the real world)
in the sense that there must exist particles charged under any other kind of force for which the force of gravity is subdominant; their mass/charge ratio is smaller than for extremal black holes and the overall force between two copies of such a particle must be repulsive. This statement may be (and has been) justified by many arguments, for example:
- the entropy bounds and the absence of remnants
- the ability of extremal black holes to decay unless they are BPS
- the continuous character of the magnetic monopole charge of all objects that can be described as black holes
- the verification that the rule is satisfied in all classes of string theory backgrounds that have been looked at
According to our knowledge of string theory, it seems that there also cannot exist any backgrounds which only contain massless gravity but no massless gauge fields or scalars. See page 6 of the Swampland paper, for example. Pure quantum gravity does not seem to be an option. Moreover, we know that in the real world around us, gravity is not the only force - and the strength of the other forces does not go to zero, not even at the Planck scale.
Let us accept that pure gravity is not the final goal. Can it be a step towards getting a full theory, after we "add" the other forces such as electromagnetism as perturbations?
The answer is a resounding No.
When you add a force that you want to treat perturbatively, which should be possible if the success of QED is reproduced by your quantum theory of gravity and electromagnetism, then you are expanding around "g=0" where "g" is the gauge coupling. In quantum gravity, there is a new ultraviolet cutoff "g.M_{Planck}" above which the effective theory breaks down. If "g" goes to zero, then this scale goes to zero, too. The theory therefore breaks down at all scales. You can't expand around the point where gravity is the strongest force because a quantum theory of gravity in which gravity is stronger than other forces is inconsistent.
In unified theories - i.e. in string theory - this problem is avoided because the same coupling "g" also governs the strength of gravity, and setting "g=0" implies that "M_{Planck}" goes to infinity and the cutoff scale remains finite.
Well, I don't expect that the people who try to study "pure quantum gravity" will suddenly realize and accept these observations. But I do hope that many other readers will get the point. When the role of quantum mechanics is considered, other forces cannot be neglected when we try to include gravity. All forces must be studied simultaneously which is why a unified theory is necessary for a description of quantum gravity to be consistent.
This is the 17th known reason why string theory is the only tool to study quantum gravity, beyond the semiclassical approximation, that we have as of January 2006.
| | 13 snail comments :
Lubos:
The notion that gravity is the weakest force you find in the natural world is absolutely wrong. Quite to the contrary, you keep observing the gravity force to be the strongest:
You see apples fall to the ground all the time. But do you ever see an apple flying to the sky, because it was attracted by electrical force? You observe planets circling the sun due to gravity as the norm. But people never observed a planet being expelled from a star system due to electrical repulsive force, or be attracted to the sun due to attraction of charges. Do you? Occationally you do see a few cases where the EM force is stronger. But overall, there are much more observations of stronger gravity force than anything else.
Now you may argue that the gravity force between two commonly known fundamental particles are much weaker. But you can NOT define the coupling constant for gravity until you have defined the proper mass scale, so that the gravity coupling constant becomes a dimensionless number, just like alpha is.
But here is where the theoretical physicists have been strange! In all other occasions, they insist that the natural scale for mass, as for space and time, is the Planck scale. So one Planck mass is the proper mass scale. But then, if you use one Planck mass to define the gravity coupling constant, it is exactly one, so much stronger than the alpha of EM force, which is about 1/137.
But NO, although they insisted on Planck scale on everything else, when it comes to defining the gravity coupling constant, they changed their mind and refuse to use the Planck mass as the mass scale. Instead, they use something much smaller, something like the proton mass or things like that. Isn't that double standard?
The correct natural mass scale, as I discovered, is one that when multiplied by the alpha, gives a mass value that equals to the electron mass we know.
The strength of gravity is defined by the Mach Principle. Consider any particle. The interaction between the particle and the rest of the universe gives an exact total gravitational potential energy which is exactly equal to the mass/energy of the particle. That, is where the equivalence principle comes from, one that says gravity mass and inertia mass is always identical. I have almost everything figure out already. Remember I gave out the formula that G = 1/(2N). Now I can explain completely where that came from, and have also reconciled the remaining 2% discrepancy between theoretical value of G and actual measured value.
Finally, the hypothesis you raised together with Vafa is uninteresting and unworthy of discussion. A counter example could easily be proposed by a 6 year old little girl. A black hole, for it exhibits no internal property or internal structure at all, can hence be regarded as one single particle (that's what "particle" means). Such a particle can give you any value of M/Q you want.
Quantoken
I read the paper yesterday night, but I was unable to meet some useful comment to do so I refrained from just joking at the 01001 number. BTW, I haven't read it when I did the comment about decays.
As for semiclassical and classical limits, I would like that any comment entering in this discusion made explicit all the constants, no h=c=1 in the limit where c->0 or so.
About gravity, I thought I was already done with the field, my only contributions being the Quantum Haiku gr-qc/0404086 and the d=24 normalization paper physics/0409022. But here comes a related thinking your paper suggested me in the bed. I supposse that in the limit c->infinite the spin-2 mediator could be replaced by an scalar, could it? But also in the limit h->0 only scalars can remain (it is different in the classical limit n->infinite). So are there two differents ways to recover Newtonian gravity from quantum gravity?
er d=26 of course :-(
Dear Quantoken,
the Earth attracts the apple because it is a combined gravitational action of 6 x 10^{24} kilograms of matter, and all of which has the same sign of the force.
Because the Earth is electrically neutral, it does not exert any significant electrostatic force because the contributions cancel. But one can still take a piece of magnet and this small magnet exceeds the gravity of the whole planet. You can ask your nurse to help you with this experiment.
Gravity at the fundamental level is 10^{44} times weaker or so, and ask someone to calculate this ratio for the electrons.
Best wishes
Lubos
Dear Leucipo,
when we study forces, we still look at at quantum relativistic physics where all adult people use and always can use the c=hbar=1 units, and we leave discussions about nonrelativistic physics and Apples to Quantoken.
If you really need to recover the c,hbar factors, there are many good high school textbooks of physics.
All the best
Lubos
This is support of conjecture of finiteness of the volume of moduli spaces. But what about NON-SUSY, NON-GEOMETRIC or NON-KAHLER generic flux compactifications??
Dear Planckeon,
thanks for your interesting question. Your question is slightly ambiguous because it has no verb. What about them? They're doing fine, thank you.
If you ask whether they have moduli spaces, then the generic nonSUSY ones do not have one; nonGEOMETRIC backgrounds tend to have less moduli (but they still have moduli if they're e.g. points on the regular moduli spaces, such as Gepner models); and the moduli of nonKähler compactifications are claimed to exist by some colleagues, but disputed by others.
If you ask whether the bound on the strength of gravity should hold for these three NON classes, the answer is Yes. It should hold generally in quantum gravity. If you asked whether it has been checked on examples, the answer is Partially yes - the heterotic discussion, for example, does not assume Kählerity, geometric interpretation, or spacetime supersymmetry.
All the best
Lubos
Lubos,
You really do need to see http://feynman137.tripod.com/
.
See my blog for Prof Josephson's joke:
From: "Brian Josephson"
To: "Nigel Cook"
Sent: Wednesday, January 04, 2006 4:59 PM
Subject: Re: mathematics
... An old Cambridge story, concerning a person who found himself sitting next to the taciturn Prof. X (X being variously named as Dirac, Stokes ..) at dinner.
Person sitting next to X: "someone has bet me I won't get more than 2 words out of you tonight"
Prof. X: "You lose!"
=b=
* * * * * * * Prof. Brian D. Josephson :::::::: bdj10@cam.ac.uk
* Mind-Matter * Cavendish Lab., J J Thomson Ave, Cambridge CB3 0HE, U.K.
* Unification * voice: +44(0)1223 337260 fax: +44(0)1223 337356
* Project * WWW: http://www.tcm.phy.cam.ac.uk/~bdj10
* * * * * * *
Thanks to Professor Josephson for the joke above! {See footnote to this post for the context of Josephson's email.} The entire physics community is tactiturn and unamused at any innovation. It is nearly as funny as Dr Woit's rip-roaringly scientific response: Thanks to Professor Josephson for the joke above! {See footnote to this post for the context of Josephson's email.} The entire physics community is tactiturn and unamused at any innovation. It is nearly as funny as Dr Woit's rip-roaringly scientific response here:
http://www.math.columbia.edu/~woit/wordpress/?p=215#comment-4081
‘(1). The idea is nonsense. (2). Somebody thought of it before you did. (3). We believed it all the time.’ - Professor R.A. Lyttleton's summary of inexcusable censorship (quoted by Sir Fred Hoyle in ‘Home is Where the Wind Blows’ Oxford University Press, 1997, p154).
Don't be a tactiturn loser, Lubos!
Nigel
Lubos said:
"Gravity at the fundamental level is 10^{44} times weaker or so, and ask someone to calculate this ratio for the electrons."
Wrong! It depends on what you call fundamental level. On common dictionary of theoretical physicists, the fundamental level is the Planck Scale. At Planck scale, gravity equals to ONE, roughly 137 times stronger than EM force. On my dictionary, the fundamental scale of mass is roughly 137 times the mass of the electron, and gravity would be 1/2N, i.e., 1/(3x10^40), comparing with 1/137 for EM force. You must be calculating using the electtron mass, but in that case, the gravity is roughly 4x10^42 times weaker than EM force, your 10^44 times figure is still wrong. You would have to use a mass which is roughly 20% of the electron mass to get the 10^44 figure. And certainly if you calculate using proton mass, it's yet a different figure.
It's chaotic that theoretical physicists can't decide on what to use to calculate the strength of gravity. Some use Planck mass, some use proton mass, some use electron mass. And Lubos is using 20% of electron mass. You guys don't have a clue what is the appropriate mass scale!!! You really can't compare the strength of gravity until you have decided what is the proper mass scale.
Quantoken
Quantoken,
You need to stop talking about the strength of gravity, because it is just embarrassing for everyone. OK?
Nigel
Nigel, quantoken does raise the valid point that gravity at first glance should be stronger than EM by that 1 vs 1/137 margin. A fudge factor has to be thrown in to make gravity weaker. The justification for the fudge factor could be something like gravitons get eaten by virtual Planck mass black holes, not that I really understand that, probably cause that nasty vacuum is involved.
John,
See http://feynman137.tripod.com/
(which Quantoken dismisses without reading).
The reason for the weakness of gravity is down to mechanism. Gauge bosons are always being exchanged between charges and mass, according to quantum field theory. There are two ways they can add up, which gives the tremendous difference in forces.
Nigel
http://electrogravity.blogspot.com/
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