Quantum/relativity Duality (reload)

The Holy Grail of physics is to unite the theories of Relativity and
Quantum Mechanics.

Relativity is the theory of the Very Large- cosmic scale space, time, mass and energy.

Quantum Mechanics is the theory of the Very Small- subatomic
scale particle interaction, charge and spin.

There is a concept of particle/wave duality in which the framework of wave mechanics can be translated into a more
particle-like observation, and vice-versa.

Could the duality concept be applied to Quantum/Relativity?

So, systems are actually both quantum mechanical and relativistic unless you make a measurement, at which point they become very large? Start moving really fast? Shrink down really tiny?

I’m afraid I don’t quite follow you… :slight_smile:

Well…I mean, you can observe a phenomena as a particle or
as a wave, but not both simultaneously.

You can observe a position or a direction, but not both simultaneously.

I take it you cannot simultaneously observe a phenomenon as both Quantum AND Relativistic, unless you use some kind of
translational formula like Duality.

OK the particle wave duality is a little bit of a misnomer the mathematical model of quantum mechanics is described in terms of wave functions these wave function when viewed from a macroscopic level are predicted to have the properties one would associate with particles. So there is no duality there however is a difference in perceived behavior depending on scale.

The uncertainty principle is one of the cornerstones of quantum mechanics and describes one of the inherent properties of the model using this, as a comparison when comparing different models for the same system is not really valid.

The present work in this area is more closely related to the wave particle concept where by a model is developed that will behavior in a quantum manner at high energy levels but retain all of the properties of relativity (or super gravity depending on your school of physics) at low energy levels.

Well, first of all, it should be noted that relativity and quantum mechanics are not mutually exclusive. There are relativistic quantum effects. In fact, I have a book on my shelf entitled “Relativistic Quantum Theory”, which I got for free somewhere. (I’ve never opened it.)

Secondly, wave-particle duality is based on the concept that both are the same thing, in different situations. Heisenberg Uncertainty (momentum and position not being simultaneously measureable) is based on the fact that momentum and position are mathematically coupled (conjugate variables).

It’s not clear how the analogy extends to relativity and quantum mechanics, as currently formulated. For that matter, why is it assumed that these theories can be unified? My hunch is that any unified theory would be unwieldy to the point of being impractical, and we’d keep doing things the way we are now.

On rereading, I should mention that in the second paragraph “both” refers to both waves and particles, not quantum mechanics and relativity.

By that, are you meaning every particle has a wavelength? Still, for certain particles, the quantum wave function collapes, and it forms a particle. That seems like duality to me, so I guess I’d disagree that it is a misnomer. Do you have a cite for that?

Yeah, I would agree that it is not a misnomer to refer to particle/wave duality. Depending on the way a phenomenon is manipulated and observed, these wave vs. particle properties generally cannot be observed simultaneously.

But yeah, I don’t think this applies to relativity and quantum theory. I think the reality there is that 2 very different environments led to drastically different approaches to modeling. It is always important to remember that these are all just models created by people and there is no “correct” model for the universe. Some are just better than others.

So I think the fact that there are some gaps between relativity and quantum theory really comes down to the fact that we don’t have things all worked out yet. :slight_smile: I don’t see any reason why a new model couldn’t come along that encompasses both.

Actually every particle does have a wavelength–the De Broglie wavelength. In fact, between measurements a particle only exists as a wavefunction, unfortunately no one knows what a wavefunction really is.

When a measurement is made the wavefunction collapses and a particle is observed. Having said this I’m not sure what Brit is talking about.

This is what string theory is all about.

First of all, there are two different theories of relativity. The simpler one is Special Relativity (SR), which combines space and time into a single entity, and is mostly used to describe what happens when things move very fast. All of modern physics is consistent with SR. On the other hand, you also have General Relativity (GR), which contains all of SR, and also describes how mass interacts with spacetime, thus producing gravity. The current theory of GR is not consistent with the current theory of quantum mechanics, so in order to unify them, one or both will need to be changed somehow. And there must be some sort of unification: When, for instance, a black hole evaporates down to a sufficiently small mass (just how small is “sufficiently” is not known, but a good guess is around the Planck mass), something has to happen, but we don’t know yet just what that something would be.

I’m not sure that the concept of duality is a useful one here: When you’re working with quantum mechanics, you don’t care whether you’re describing waves or particles. You do all the math the same way, and then, at the end, you decide whether waves or particles will be more convenient for expressing your answer. With GR and QM, though, it’s not just a matter of description: The intervening math is completely different.

“This is what string theory is all about.” – Ring

Mebbe better to say that this is what string theory aspires to be, since the mathematical complexity of string theory has left it as of yet unable to provide a model for any observable phenomenon. :slight_smile:

I was attempting to say what Chronus said. The particle wave duality is never really there. Sometimes it makes more sense to think in terms of particles sometimes in waves but there is never a duality of form mealy of interpretation. I have always held that the concept that matter was both a ‘real’ wave and a particle at the same time was both misleading and unnecessarily confusing.

Some issues to overcome in a combined theory
The basic issue of the role of space-time in the theory. In quantum mechanics space-time is a passive unchanging background in which quantum effects take place while in General Relativity space-time is a dynamic component bound into the model.
The infinities that tend to crop up when describing things like particle splitting recombination sequences and the fact that previous techniques to remove the infinities from the models are proving ineffective or very difficult to quantify correctly.

I must admit I am a General Relativist moving towards Quantum Theory rather than the other way around and that I really no not like matter field theories.

As for string (super string + derivative theories) that would take quite a bit of room to cover.

The good news is we are working on it the bad news is that we aren’t there yet (or even 100% certain we are on the right road).

I’d like to add something to what Britt said.

Britt states that in QM, Space and time are just a background
environment in which phenomenae are observed and measured,
while in GR, space and time are combined together as a dynamic field; part of the phenomena itself.

In GR what is observed is relative to the observer.
In QM, the observer is inseperably linked to the observed, thus,
both observer and observed are combined together as a dynamic

One more shot at the ‘wave/particle duality’ thing: It really doesn’t exist, because ‘waves’ and ‘particles’ are just concepts we humans have made up. Kind of like ‘pure evil’ and ‘perfect husband’. Or ‘pure point guard’ and ‘pure shooting guard’, if you’re a basketball fan. We like to use the concepts because they’re easy to think about and understand, but there’s no reason that the real world falls neatly into our concepts.

Photons, electrons, etc. just ARE. Sometimes when we humans describe what they’re doing, it’s convenient to talk about them like waves and sometimes like particles, but that doesn’t mean the electrons are any different. Likewise, when John Stockton (the basketball player) passes to the open cutter on one possession, and hits a long jumper on the next, it doesn’t mean he’s magically transformed from a ‘pure point guard’ to a ‘pure shooting guard’. He’s still who he is, just in the one time, our mental model of ‘point guard’ applies better, and in the next ‘shooting guard’ is a better fit.

As Chronus pointed out Quantum mechanics is entirely consistent with Special Relativity which is the part of General Relativity that deals with reference frames.

There is still some debate about the mechanism required for the wave function to collapse, I am presently working on a reference frame based model in which the act of observation is removed. There have been several attempts at resolving the collapse before all of which have some outstanding objections against them. For reference the canonical model at present is The Copenhagen Interpretation.

  1. The uncertainty principle of Heisenberg (1927): this includes wave-particle duality, the role of canonically conjugate variables, and the impossibility of simultaneously measuring pairs of such variables to arbitrary accuracy.
  2. The statistical interpretation of Born (1926): this includes the meaning of the state vector given by the probability law (P=YY*) and the predictivity of the formalism only for the average behavior of a group of similar events
  3. The complementarity concept of Bohr (1928): this includes the “wholeness” of microscopic system and macroscopic measurement apparatus, the complementary nature of wave-particle duality, and the character of the uncertainty principle as an intrinsic property of nature rather than a peculiarity of the measurement process.
  4. Identification of the state vector with “knowledge of the system” by Heisenberg: this includes the identification itself and the use of this concept to explain the collapse of the state vector and to eliminate simple nonlocality problems
  5. The positivism of Heisenberg: this includes declining to discuss “meaning” or “reality” and the focusing of interpretive discussions exclusively on observables

Those last two points are still somewhat contentious, and the last point should be noted when interpreting the wave-particle duality

Special Relativity deals with reference frames, but General Relativity does not? I’m trying to make sense of that, but I guess I need some help.

That was poor phrasing. Britt put it better earlier:


Special relativity provides the “passive unchanging background”. In other words, in SR spacetime is static. In GR spacetime is dynamic - its curvature changes as masses move around.

As far as reference frames, SR allows you to work in any frame that is moving at a constant velocity with respect to an inertial frame. But in GR, you can work in any coordinate system and the laws of physics will be unchanged. For instance, you can choose a “you-centered” frame - measure all distances from you, and time from when you were born, according to your watch (even if it’s running slow), and the equations of GR will still work. They’ll be impossible to solve, but they’ll still work.