Quantum/ Relativity incompatibility?

[xhalmers_860]

Hi,

Not totally top notch on physics- I just studied it till in school till I was 18. I am aware, however, that there is some sort of incommensurability of the two main strands of theoretical physics- quantum and relativity. Could someone please tell me what that is?

And more to the point, for my purposes, are there any actual experimental consequences of this incompatibility? Does one work in some circumstances and the other not? Or do they both fit the data in all cases, and the incompatibility is really just ontological?

I would really appreciate some help on this.

 

[Astronuc]

To what incompatibility is one referring?

I don't believe there is an incompatibility between QM and relativity.

Is one referring to SR or GR or both?


Certainly relativistic effects are observed in high energy particles, where kinetic/total energy >> rest mass.

 

[xhalmers_860]

I might be wrong...

But things like this suggest some sort of problem...

"[URL
"General relativity has yielded a wealth of insight into the Universe, the orbits of planets, the evolution of stars and galaxies, the Big Bang and recently observed black holes and gravitational lenses. However, the theory itself only works when we pretend that the Universe is purely classical and that quantum mechanics is not needed in our description of Nature. "[/URL]

 

[staf9]

Do you mean the search for a http://en.wikipedia.org/wiki/Grand_unification_theory" ? Or, as I hate to call it, a "Theory of Everything"?

 

[xhalmers_860]

Well, yes. Maybe it would help if I told you why I'm asking these questions. I am just confused as to why we can't have both quantum and relativity- why do we need unification? Are there any non- aesthetic (i.e. experimental) reasons for preferring a unified theory?

 

[starkind]

Hi,

Not totally top notch on physics- I just studied it till in school till I was 18. I am aware, however, that there is some sort of incommensurability of the two main strands of theoretical physics- quantum and relativity. Could someone please tell me what that is?

And more to the point, for my purposes, are there any actual experimental consequences of this incompatibility? Does one work in some circumstances and the other not? Or do they both fit the data in all cases, and the incompatibility is really just ontological?

I would really appreciate some help on this.

General Relativity breaks down on both ends...it cannot describe what happens near the singularities, which are predicted by GR mathematics. GR fails us when we want to know what is going on near black holes and the big bang, and also in the realm of the very, very small, where quantum uncertainty breaks all the rules.

On the other hand, the standard model of particles gives us a really good quantum description of matter, but has no description of gravity.

This conflict is mostly a matter of theory, especially in high energy physics, which deals with things that are very very small. However there are some anomalies on the cosmic scale also, such as the fact that one of the early space probes (ummm, voyager 4?) is not where it is supposed to be, according to GR mathematics.

Einstein didn’t like quantum flippery, but he was unable to show a theory of everything based on GR. Nowadays, there is considerable interest in the idea of quantum gravity, which may involve changes in the standard model, or in GR, or in both.

Hope this helps

 

[starkind]

Are there any non- aesthetic (i.e. experimental) reasons for preferring a unified theory?

The grand unified theory, GUT, is pretty well accepted now, I think. Unification of electromagnetics, which governs how our world works, and the weak force, which holds protons and neutrons together in atoms, has been done for some time now, and in the last couple decades or so the strong force, which holds quarks together in large particles like protons an neutrons, has been shown to be the same as the electro-weak, at very high energies.

What is lacking for a theory of everything is an addition of gravity into the mix, which some people think would be very interesting. Remember those flying cars on The Jetsons? Or the floating skateboard in Back to the Future? Or the warp drive on Star Trek? Or the ground scooters in Star Wars? It certainly would be interesting if we could control gravity as well as we control electricity and chemistry, wouldn't it?

 

[staf9]

Right now the big parties at research institutions are string theorists and Loop Quantum Gravity (LQG).

To clarify my last post, GUT usually refers to the prediction that electromagnetic and weak nuclear (which are collectively known as electroweak), and strong nuclear forces are "fused" into a single field at high energies.

Theory of Everything refers to the addition of gravity into this mix, or the unification of gravity with the electronuclear forces united by GUT. Getting into dark energy/dark matter/universal inflation is also touched upon in cosmology.

In GUT, there are a variety of models and theories, off the top of my head I can think of the Pati-Salam, left-right (chiral symmetry), and Georgi-Glashow. These 3 are all for GUT only and even though there's not a single one which is universally accepted, I believe the Pati-Salam model is in the lead right now.

 

[Timo]

And more to the point, for my purposes, are there any actual experimental consequences of this incompatibility [between QM and GR]? Does one work in some circumstances and the other not? Or do they both fit the data in all cases, and the incompatibility is really just ontological?

The point is: There is almost no experimental scenario where complete ignorance of one of the two theories wouldn't already give perfect results. When you shoot two electron onto each other, you can completely ignore gravity. When you calculate the motion of stars or planets, you can completely forget about QM. There are very few scenarios in which we currently expect a unified theory to be important:
- Very early stages of the universe: You cannot create these conditions, but we actually live in a world that came out of these conditions and hence already have/are the experimental outcome. Combined with that we seem to reach the energy limits of colliders (the historic experimental device of particle physics) this is the reason why the interest of particle physicists in cosmology has grown huge.
- Black holes can have an arbitrarily large deformation of spacetime. Arbitrary then naturally means that it might not be negligible for the interactions of particles, anymore. The bad thing is that we've (afaik) not even directly observed a BH, less figured out how to do experiments with it.

The big problem with quantum gravity, both for experimental verification of predictions and in my personal opinion also for justifying effort put into it in the first place, is the lack of conditions in which we expect it to be necessary.

In short: The lack of experimental consequences can currently be seen as the biggest problem for that field.

-----

I don't believe there is an incompatibility between QM and relativity.
Is one referring to SR or GR or both?

GR, as already the Standard Model of particle physics implements SR. More particularly, the implementation of gravitational interaction (GR being a description for gravitational interaction) via a quantized field.

-----

The grand unified theory, GUT, is pretty well accepted now, I think.

Depends on "by whom?". Generally, I'd spontaneously disagree, at least if "accepted" means more than "ok, it's a nice idea" (just ask an experimentalist whether he is convinced that a particular GUT model was implemented in nature). Other than that, staf9 sums up what I additionally wanted to say about that statement:

In GUT, there are a variety of models and theories, [...]. These [] are all for GUT only and [...] there's not a single one which is universally accepted, [...].

It certainly would be interesting if we could control gravity as well as we control electricity and chemistry, wouldn't it?

Or as we control the strong force .

-----

Right now the big parties at research institutions are string theorists and Loop Quantum Gravity (LQG).

I think it's rather somewhat like this:
- The big parties at (physics) research institutions are solid state physicists.
- The big parties at particle physics institutions are SM physicists (B-physics, Higgs-search, don't know what else).
- The big parties at theoretical particle physics institutions are QCD people (that one is really just an impression of mine).
- The relatively little amount of people doing quantum gravity research are mostly stringers. A few are lqg people.

 

[xhalmers_860]

Thanks guys. Timo, that was particularly useful. I'm a philosopher really, and am doing an essay on Pierce; a father of pragmatism and advocate of the scientific method. The pragmatist theory of truth is generally that a hypothesis only makes sense in terms of a willingness to undertake certain 'habits of action,' therefore, if you are unable to say what you would do differently, that is what the actual experimental difference would be between two theories, they are the same with regards to their truth.

The interesting thing with this (that he didn't predict) is that it doesn't consider new scientific theories that predict the same experimental results to be superior. Unless we refer to simplicity (and, for him, only in terms of how easy it is to understand, and quick to disprove if it is wrong) then there is no way to argue for a substituting new theory that yields the same results, like string theory. What I was interested in was that if we accept that scientific hypotheses only signify certain predicted experimental results, there is no real reason not to accept different models for different purposes- even, as you say, both quantum and gravity break apart in certain peculiar situations. Especially if using two theories turns out to be, quite bluntly, easier in a man- hours sense of the word.

 

[ZapperZ]

I would suggest that you use this thread and this sub-forum to get a better understanding of the physics, and then use the Philosophy forum for related discussions. This thread is heading way too much into the latter area without rather clear physics content.

Zz.

 

[Fredrik]

I am aware, however, that there is some sort of incommensurability of the two main strands of theoretical physics- quantum and relativity. Could someone please tell me what that is?

General Relativity (GR) is still the best theory of gravity we have. It's a purely classical theory. It describes space-time as a four-dimensional manifold, and postulates an equation (Einstein's equation) that tells us the relationship between the geometry of that manifold and the distribution of matter and energy on it. The geometry determines how things move. This famous John Wheeler quote that summarizes it pretty well: "Matter tells space how to curve. Space tells matter how to move".

So on the left-hand side of Einstein's equation, we have space-time geometry (i.e. gravity), and on the right hand side, we have matter. Now, here's the problem: We know that matter doesn't always follow the rules of classical mechanics. So the right-hand side of the equation can't really be described classically. This implies that the left-hand side (i.e. gravity) can't really be described classically either.

I can also think of other arguments, e.g. consider an interaction between two elementary particles at an energy that's so ridiculously high that the two-particle system should collapse into a black hole according to the laws of GR. We would obviously have to use a theory capable of describing both gravitational and quantum mechanical effects to predict what would happen.

 

[staf9]

I think it's rather somewhat like this:
- The big parties at (physics) research institutions are solid state physicists.
- The big parties at particle physics institutions are SM physicists (B-physics, Higgs-search, don't know what else).
- The big parties at theoretical particle physics institutions are QCD people (that one is really just an impression of mine).
- The relatively little amount of people doing quantum gravity research are mostly stringers. A few are lqg people.

Yeah, you're definitely right about solid state/SM, I should have specified quantum gravity research back there.

 

[meopemuk]

I am aware, however, that there is some sort of incommensurability of the two main strands of theoretical physics- quantum and relativity. Could someone please tell me what that is?

The contradiction between quantum theory and special relativity is at a very basic level.

Special relativity assumes a 4-dimensional picture of the world. Lorentz transformations mix space and time coordinates of events. I.e., the time of an event in the moving reference frame O' is a linear combination of the time and position of the same event in the reference frame at rest O. This implies that x and ct must be represented by objects of similar mathematical nature.

However, in quantum mechanics time and position have very different mathematical representations. Time is a classical numerical parameter. The observable of position is represented by a Hermitian operator. The linear combination of a parameter (ct) and an Hermitian operator (x) does not make sense. So, it is not obvious how Lorentz transformations should be implemented in quantum mechanics.

Eugene.

 

[Chris Hillman]

Not totally top notch on physics- I just studied it till in school till I was 18. I am aware, however, that there is some sort of incommensurability of the two main strands of theoretical physics- quantum and relativity. Could someone please tell me what that is?

Briefly, gtr is a relativistic classical field theory. The standard model of particle physics is on the other hand a quantum field theory. The theory of EM started as Maxwell's relativistic classical field theory and was later elaborated into a quantum field theory (QFT) called quantum electrodynamics (QED), but the approach which worked there turns out not to work for gtr. QED and a QFT for quarks, quantum chromodynamics (QCD), are incorporated into the standard model along with the weak interaction.

And more to the point, for my purposes, are there any actual experimental consequences of this incompatibility?

I think the best short answer is: not yet.

Does one work in some circumstances and the other not?

Yes, existing QFTs work in scenarios in which gravitational phenomena can be neglected, while gtr works in scenarios in which the gravitational field is not so strong that the curvature approaches the reciprocal of the Planck area.

It's probably not possible to give a precise yet nontechnical explanation but I hope this will serve your purposes!

General Relativity breaks down on both ends...it cannot describe what happens near the singularities, which are predicted by GR mathematics.

It is expected that gtr will break down at extremely high curvatures, which would occur very near the putative curvature singularities which are predicted by gtr to occur in various circumstances.

GR fails us when we want to know what is going on near black holes

Careful! If you mean "near the horizon of a black hole", this is wrong for stellar mass black holes and even more wrong for supermassive black holes; the curvatures encountered in those regions are nowhere near the Planck scale. Or more precisely, as far as we know, gtr should be good in the neighborhood of the event horizon of both stellar mass and supermassive black holes, but we are only just beginning to test the "just outside the horizon" part of this statement.

and [near] the big bang

Careful! For example, the curvatures thought to have occurred around the time when photons could first travel freely (the CMB is the "fossil" of this "moment") were not near the Planck scale and as far as we know gtr should be good there.

and also in the realm of the very, very small, where quantum uncertainty breaks all the rules. On the other hand, the standard model of particles gives us a really good quantum description of matter, but has no description of gravity.

Correct.

The bad thing is that we've (afaik) not even directly observed a BH, less figured out how to do experiments with it.

Careful, depending upon what you mean by "directly observed" and "black hole", this is either wrong or terribly misleading; see
this (the author is the Astronomer Royal in the UK, and one of the leading figures in the complicated history of how the existence of black holes was transformed from an almost universally doubted notion into an almost universally accepted notion),
this,
this,
this and this.

 

[CarlB]

Chris, from the first and most recent links you gave as "this", the following quotes give the whole story on black holes:

"The evidence points insistently towards the presence of dark objects, associated with deep gravitational potential wells; but it does not in itself tell us about the metric in the innermost region where Newtonian approximations break down."
http://www.arxiv.org/abs/astro-ph/9701161

and

"While the evidence based on mass is certainly strong, there is no proof yet that any of the objects possesses the defining characteristic of a black hole, namely an event horizon."
http://www.arxiv.org/abs/astro-ph/0310692

In short, there is no evidence for black holes at this time except that GR works (except for dark matter and dark energy which Einstein and the string theorists somehow managed to overlook in making their predictions but makes up 95% of the universe's mass-energy) at weaker regions and predicts event horizons at stronger regions. Furthermore, at this time, no one has successfully combined GR and QM into a single theory.

Of the two theories, GR and QM, quantum mechanic is by far the better supported by experiment. So if the failure of thousands of brilliant physicists to combine the two theories is due to only one of them being wrong, that one is very likely to be GR. And without GR, the evidence for event horizons is non existent.

By the way, remember those calculations I made for the equations of motion around a black hole in Painleve coordinates? The ones you asked me in PM to retract as obviously incorrect? And remember the thread you got locked by *****ing about the subject, over on the General Relativity thread?

I'm sure you'll be relieved to learn that the applet I created based on my results is now being used at MIT to teach general relativity to grad students. I'm reminded of all this because my whole purpose in going to all that effort was to put together clues for how to replace GR with QFT on a flat Euclidean / Minkowski metric.

 

[friend]

In short, there is no evidence for black holes at this time except that GR works

I've seen videos of stars at the center of our galaxy being diverted sharply by an invisible object. This could not be accounted for by any other mechanism except by a black hole.

 

[tomas666]

Well, yes. Maybe it would help if I told you why I'm asking these questions. I am just confused as to why we can't have both quantum and relativity- why do we need unification? Are there any non- aesthetic (i.e. experimental) reasons for preferring a unified theory?

I'm not sure but learing one law that rule everywhere is easyier than 4 laws.For example it would be great to get gravitation that is elektromatism and strong force in one:D