Quantum Mechanics: Space-Time Existence & Geodesics

[eljose79]

-at small scales and taking into account the uncertainty principle..could we make the stament that space-time exist?..if so how it would be at a quantum scale what is the equivalence to geodesics and Rienmann tensor in quantum mechanics..?..

 

[selfAdjoint]

You have to distiguish the "flat", Minkowskian spacetime of special relativity from the "curved" spacetime of general relativity. Quantum theory has been manifestly covariant since Dirac (1927), which means it can be interpreted as taking place in Minkowski spacetime. Nobody yet has been able to create a fully quantum version of general relativity, although both String physics and various nonstring Quantum gravity proposals claim partial success.

 

[jeff]

Spacetime may be viewed as the large scale structural quality possessed by sufficiently low energy gravitational fields as described by GR. At higher energies, i.e., shorter distances, quantum fluctuations in the gravitational field wash out this structure so that geometrical notions like distance and curvature lose their applicability. What should replace them is the subject of quantum gravity.

 

[marcus]

Originally posted by eljose79
-at small scales and taking into account the uncertainty principle..could we make the statement that spacetime exists?...

No.

I found Rovelli's section 2.3.2 called "The disappearance of spacetime" a helpful thing to read, about this question.

It is on page 52 and 53 of the current draft of his book. The PDF file for the book takes 5 or 10 minutes to download and convert but then you store it on your computer's desktop and can refer to
any of the chapters. It's really useful and I strongly recommend it.

http://www.cpt.univ-mrs.fr/~rovelli/rovelli.html

The book should be out in hardcopy from Cambridge University Press sometime this year. So this draft may not always be available online.

 

[eljose79]

-In fact could our space and time a result of the statistical physics?..in fact we see space and time because they are the maximum likelihood probability of some event...that is similar to the thing that happens with Feynman interpretation of quantum physics as path integrals for h=0 the only contribution would be when dS=0 could hte same happen to space-time?...does spacetime exist only as an statistical phenomenon?..

 

[marcus]

Originally posted by eljose79
-In fact could our space and time a result of the statistical physics?..in fact we see space and time because they are the maximum likelihood probability of some event...

I believe this is a correct interpretation of the physical picture given by Loop Quantum Gravity.

For example see Rovelli's book page 269 in the Conclusions chapter,
Chapter 10 section 10.2 where he is summing up.
"Physical space is a quantum superposition of spin networks."

The evolution of states of space is a quantum superposition of spin foams, analogous to a sum over histories.

One adds up all the spin foams which can mediate between one spin network and another. There is not any strict analog of "spacetime", just as there is in reality no classical trajectory followed by a particle. There is a sum of all possible trajectories. This looks to us like "spacetime".

I am not claiming to know that Rovelli is right or that you are right. I merely say that what you are describing is the conclusion about spacetime reached by the LQG model---which a bunch of people are working to complete. Also on page 269 Rovelli briefly summarizes the missing and inadequate parts of the theory, also discussed elsewhere in the book.

 

[dave@yvestcom]

I'm a newbie and don't have any formal background in physics but i am learning...which brings me to my question.

If space time doesn't exist how are objects defined? If objects/matter don't exist over space time what happens to their energy? Is energy then a constant thing or is energy non-existent?

I have a bunch more questions but this is a good start. Some one please help!

Also any books or sites for beginners would be great.

 

[marcus]

Dave, a draft of Rovelli's book is available on-line for free, and there are portions of it which are non-mathematical----written in plain English to give a kind of philosophical or conceptual context and motivation.

Those plain language parts of the book are, I think, exceptional. They are only a few pages out of the whole book but they can be quite helpful in suggesting how to think about things. I will get a link in case you want to have a look.
www.cpt.univ-mrs.fr/~rovelli/book.pdf

The first useful passage is section 1.1.3 "The physical meaning of general relativity". This is on pages 9 and 10 of my purchased copy. The pages of the free online draft copy sometimes differ, but if I say "section 1.1.3" you can always find it by looking in the TOC or just scrolling thru.

Here he is not even talking about quantum gravity. He is talking about what we learn already from good old vintage 1915 General Relativity.
You could try those two pages and see if it helps. If that begins to work for you, then come back and I or somebody can point to other helpful passages.

Don't be put off by the fact that much of the rest of the book is abstract math

 

[dave@yvestcom]

thanks.

 

[dave@yvestcom]

not done yet, but i like spoilers...

Rovelli says that space time is non-existent and what we thought was space time is actually the gravitational field, but that means that the universe is not expanding it's contracting and that time (at least what most consider to be time) is not moving forward it's moving backward. (being that gravity is a force that pulls and doesn't push.) That explains energy and matter but it creates a lot more questions for me.

I know that's a really simple way of putting it, but is that what he's getting at? How is that possible?

 

[marcus]

the biggest hurdle is the first: "gravity = geometry"

the legacy of Einstein from 1915 is that the gravitational field should not be thought of as a bunch of force arrows, or in terms of force at all. the gravitational field can and should be thought of as shape or curvature built into spacetime

but there is no "outside" to spacetime, so how can you describe its curvature?

You can do that by measuring the angles of a triangle and seeing what they add up to, for instance. there are intrinsic ways to feel and measure the geometry of a place, without going outside it. Think of the 2D creatures of flatland and how they measure the geometry of their 2D world that they cannot go outside of.

so a 4D spacetime can have a geometry. That geometry is the "gravitational field". And a 4D geometry can have 3D "spatial" slices. And these slices can expand or contract--the spatial distances can get larger or smaller as you move in a timelike direction from slice to slice.

Geometry can be dynamic, it can change, it can respond to matter. Geometry guides matter along its geodesics (its shortest-distance paths) and the flow of matter bends geometry and changes its curvature.

Now if this is going to be a useful theory that we can calculate orbits with we need a mathematical representation of the geometry

So think of being given an utterly shapeless floppy 4D continuum, something with no geometry----limp as a dishrag. amorphous as butterscotch pudding. The way you endow it with geometry or shape is with a distance function, a socalled "metric". This is a mathematical gizmo that let's you establish distances. Before you impose the metric there are no distances. Now there are distances, and there are shortest paths----so you can say what a straight line is---and you can define triangles and circles and angles and areas...All this comes from having a metric.

Einstein taught us that the metric is the gravitational field. There is no need for another thing. Gravity is nothing else than simply the geometry itself.

And then he taught one more trick, which is to GET RID OF THE PUDDING. So like the smile on the cat after the cat is gone, you have ONLY THE GEOMETRY. This is done by a math trick which you don't have to worry about. You call two metrics equivalent if you can morph one into the other, along with the matter that gave rise to it. And then the geometry matter combination is an equivalence class---as set of possible versions each of which can be morphed into the others

And Einstein called this morphing trick "general covariance". And he said "the principle of general covariance deprives space and time of the last shred of objective reality" or physical existence. In other words "we got rid of the pudding" or the rubber, or the chalkboard, all there is left is the geometry itself".
He thought that was good.

So you said you liked spoilers. If you read Rovelli, he talks in section 1.1.3 about a whale. All the other fields, the electric field the various matter fields etc etc they all live on the geometry, which is the gravitational field. There are no "points". There are only relations, fields living on fields.
We can temporarily define points for convenience, like the point where something occurred. where two things collided, where a certain curvature was achieved. But that point has no objective existence. It could be morphed to somewhere else, and everything along with it.

fields live nowhere but on other fields. This is the difficult thing to accept. Everything else is just an illusion in your eyeball and your mind.

This difficulty is why one should read Rovelli section 1.1.3, the story about the whale and the other animals. Be easy on yourself, and gradual, avoid sudden shocks.

It's only two pages after all.

 

[dave@yvestcom]

which brings me to my original question... is energy constant or non-existent?
gravitational field replaces space time, gravity is the metric to keep track of things and is not an actual force,..right? so where does energy come from?

 

[dave@yvestcom]

This completely abandons the mass energy equivalence.

 

[marcus]

This completely abandons the mass energy equivalence.

Everything we are talking here is explicit 1915 GR, which was an extension of 1905 special rel. The massenergy equivalence arose in 1905 SR. One cannot seriously claim that 1915 GR "abandons" it
I think I am not communicating very well with you and so I will let other people try.

 

[dave@yvestcom]

I understand thank you for your help so far. I am a newbie as I said before so things are not as apparent to me as I would like.

I guess my real question was, where does the energy come from to move mass across a distance?

 

[marcus]

...
I guess my real question was, where does the energy come from to move mass across a distance?

Other people may want to respond, and might do a better job in this instance. My suggestion would be that you try reading in the book first rather than getting spoilers.
After you have read a couple of pages from section 1.1.3 (and anything else that catches your fancy) come back and let me know and I will point you at another short section or two, another two or three pages----of ordinary plain English explanation.

You seem to think that when the geometry changes and the distance between two masses has increased it somehow means the masses have "moved".
Thru what have they "moved"? since neither one may have gotten closer or approached anything? This is an example where there should be another useful section of Rovelli. But I don't want to try to find and recommend any further reading until I am sure you have digested the first.