# The Four Fundamental Forces

I'm just trying to get a few things straight as I delve into the world of quantum physics and string theory. First of all, what does it mean when someone says two forces combine, such as the electromagnetic and weak force as the electroweak force? Does that mean that the particles are the same or what? Second of all, why does gravity not fit with quantum mechanics? Is it because the concepts of time and distance are strange when discussing electrons and other subatomic particles? Thanks.

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I'm just trying to get a few things straight as I delve into the world of quantum physics and string theory. First of all, what does it mean when someone says two forces combine, such as the electromagnetic and weak force as the electroweak force? Does that mean that the particles are the same or what?
What that someone probably means is that the coupling strengths of the different forces get closer and closer together and eventually become equal at some certain energy. (The coupling strength is a number that pops up in the mathematical theory of a fundamental force that, roughly speaking, represents the strength of that force. It depends on the energy of the particles that are exerting the force on each other.)

For the electroweak force specifically, though... forces are "carried" by particles which we call gauge bosons. When two particles exert, say, an electric/magnetic force on each other, the information about this force is transmitted from one to the other by a photon, the "carrier" of the electromagnetic force. The weak force actually has 3 gauge bosons, which we call the W+, W-, and Z0. It turns out that the Standard Model predicts all 4 of these particles from the same mathematical principle.
Second of all, why does gravity not fit with quantum mechanics? Is it because the concepts of time and distance are strange when discussing electrons and other subatomic particles?
The main reason physicists seem to have is that a quantum theory of gravity is non-renormalizable. And what I mean by that is: you probably know that we are able to explain the electromagnetic force, the weak force, and the strong force using a quantum theory (the Standard Model). One of the problems people encountered when they were developing this theory is that the values it predicted for certain physical measurements (like the mass of a particle) were infinite. Eventually they found a sensible way to adjust the theory to make finite predictions; this technique is called renormalization. But it doesn't work for gravity.

It has nothing to do with time and distance, by the way. The Standard Model does rely heavily on special relativity, and there's no problem there.

tom.stoer
... why does gravity not fit with quantum mechanics? Is it because the concepts of time and distance are strange when discussing electrons and other subatomic particles?
First let me say that I agree with the reasoning regarding (perturbative) renormalizibility.

In addition there is something true about you concern regarding concepts of space and time. In order to formulate a quantum field theory one uses a given background structure called spacetime, constructs field operators on top of it and uses spacetime in order to specify commutation relations, positive and negative frequencies (particles and antiparticles) and things like that. These concepts definitly fail as soon as one takes dynamical spacetime time into account, as this invalidates what standard QFT used to use as its foundations.

Regardless which "candidate theory" of quantum gravity will eventually turn out to be the correct one: there are attempts to formulate gravity as a gauge theory (which has not an identical but at least a similar structure) as other gauge theories. Therefore the mathematical structures come closer toeach other; examples are Poincare gauge theory, LQG and SUGRA

bapowell
Yes, I would say that time and distance do have very much to do with it. Even quantum field theories in curved spacetime are notoriously difficult to build due to the lack of global time-like killing vectors in general spactimes. There are also problems related to the existence of fundamental cutoffs (ie possible discretizations of spacetime) that would force us to change the way we currently understand special relativity.

why does gravity not fit with quantum mechanics? Is it because the concepts of time and distance are strange when discussing electrons and other subatomic particles? Thanks.
The non-renormalizability is I think more the description of "how" it does not fit. The question still remains why. (and is renormalization even a sound game?)

The root cause of why, is I think also debatable. Any idea of the root cause of why, probably implies a specific research program.

One the more basic observations is that GR and classical physics in general, are resting on a different foundation. Although SR and GR, did away with some of the absolute notions of space and time, it still is a "classical model" of relativity.

QM OTOH is a measurement theory, but it's not an intrinsic measurement theory, it's rather based on "objective statistics" that is well suited for particle physics experiments, where concepts such as preparations and repeating experiments can be made sense out of.

The two conceptuals worlds just don't mix unambigously. The usual quantization procedure, usually starts from a classical model and then applies some canonical quantization scheme is itself a "semiclassical" construct, that even in the current physics is not conceptually coherent.

Most approaches try to "tweak" the current standard methods, in different directions, say tweaking the classical models, tweaking hamiltonians etc. But not that many try to tweak the frameworks.

I think the "success" of SM + QM in QFT and the standard model does not prove at some deep conceptual level that the framework is correct. It is I think more likely just an effective success. In this sense I think thta the success of SR + QM is somewhat of a "coincidence" that has given us false confidence. The conceptual issues are there also in SR + QM, it's just that we are maybe lucky to pull a somewhat working effective theory out of the mess after renormalization.

/Fredrik