# GR correspondence to reality

1. Aug 26, 2009

### Force1

I am interested in the correspondence between reality and the mathematics of spacetime and wonder if that is an issue with anyone else? How is the question of correspondence handled in teaching students about General Relativity?

I characterized the issue of correspondence as follows and wonder if I understand it correctly:

Is it correct to say:

General Relativity says that space and time are physically coupled into geometry of spacetime where points in time are events and spacetime connects mass, energy, time events and space into a physical geometry of all points in the universe where each point is fixed in the geometry of spacetime. Then at any given time, mass occupies its current point in spacetime and the EFEs describe how that mass will move, i.e. which point it will move to next. Given that geometry and motion as reality then as the universe expands it increases in volume and there is new space added as expansion proceeds because there are new points in spacetime that correspond to that expansion. That is the way the universe occupies all available space and why spacetime at this point, given accelerating expansion, would be considered open and finite and potentially infinite, i.e. able and likely to expand infinitely.

Is that a proper characterization of what spacetime is? Can it properly be referred to as a lattice of spacetime points that began with the onset of spacetime from a Big Bang type event and within which the universe is causally connected to the Big Bang event?

If so is it valid to wonder if there is a perfect correspondence between spacetime and reality i.e. is spacetime a reality or is it the best mathematical representation of the effect of gravity but not reality itself?

2. Aug 26, 2009

### Force1

Let me take this a step further before any replies.

If the description of GR above is correct then it works as described if there was a beginning of spacetime at the Big Bang event. If the Big Bang event was preceded by any circumstances where space, time, matter and energy already existed then no big deal because wouldn’t we be able to consider it reasonable that spacetime would be “reset” in the “locality” of our observable expanding universe, making everything we observe causally connected to our local Big Bang event even though there would have been preceding circumstances causally connected to another locality until our Big Bang event occurred within or from that preceding locality?

How would this "locality" approach to considering GR affect the question in the OP about the correspondence? Couldn't it be said that using the "locality" perspective, then GR could be reality even if spacetime was not being created as expansion occurs?

3. Aug 26, 2009

### Force1

I'm sure that there is something terribly wrong with the questions in this thread .

Let me break down the OP and first see if anyone will answer the first part:

Is it correct to say:

General Relativity says that space and time are physically coupled into geometry of spacetime where points in time are events and spacetime connects mass, energy, time events and space into a physical geometry of all points in the universe where each point is fixed in the geometry of spacetime. Then at any given time, mass occupies its current point in spacetime and the EFEs describe how that mass will move, i.e. which point it will move to next. Given that geometry and motion as reality then as the universe expands it increases in volume and there is new space added as expansion proceeds because there are new points in spacetime that correspond to that expansion. That is the way the universe occupies all available space and why spacetime at this point, given accelerating expansion, would be considered open and finite and potentially infinite, i.e. able and likely to expand infinitely.

Is that a proper characterization of what spacetime is?

4. Aug 27, 2009

### Force1

I'm more convinced today than I was yesterday that there is some disconnect between this thread and the rest of this General Relativity forum. The reason I suspect a disconnect of some kind is that almost every new thread gets a mentor or learned opinion in response.

OK, I am losing hope that my question will be answered but I am now wondering if someone would clue me in as to why the question seems to be a "disconnect" from the rest of the forum questions which are routinely answered.

5. Aug 27, 2009

### A.T.

The later is definitely true, the first is completely irrelevant to physics.
For questions about what is real you schould try a philosophical forum.

6. Aug 27, 2009

### tiny-tim

Hi Force1!
Sorry, but that is completely wrong

there are no new points in spacetime when the universe expands …

's jus' the same borin' ol' points as before

7. Aug 27, 2009

### Force1

I appreciate the response. I withdraw the references to reality and withdraw the notion of correspondence. Let me try again on my paragraph characterizing the nature of GR considering Tiny-tim's response.

Is it correct to say:

General Relativity says that space and time are physically coupled into geometry of spacetime where points in time are events and spacetime connects mass, energy, time events and space into a physical geometry of all points in the universe where each point is fixed in the geometry of spacetime. Then at any given time, mass occupies its current point in spacetime and the EFEs describe how that mass will move, i.e. which point it will move to next.

If I stop there is it a proper characterization?

8. Aug 27, 2009

### A.T.

Physics is about calculation not about characterization. It describes by math and not by many words without a clear meaning.

9. Aug 27, 2009

### Force1

That is not exactly true but I'm not trying to prove anything. I withdraw the unclear words.

10. Aug 27, 2009

### Fredrik

Staff Emeritus
A theory of physics such as SR or GR is defined by a mathematical model and a set of axioms that tells us how to interpret the mathematics as predictions about the results of experiments. In both SR and GR, the mathemathical model (of what we intuitively think of as space and time) is a smooth manifold with a metric. That manifold is what we call "spacetime".

You can look up the definition of a manifold, but you'll have a hard time finding the axioms that actually define the theories. The closest thing to a complete list I've seen was in a text written by a philosopher whose name I can't remember. Perhaps someone can remind me. His (her?) name begins with an M. Something like Malerin, Melamin,...

Very badly or not at all.

Your description of GR isn't very good to be honest. Unfortunately I don't have time to write a better one now. Regarding the part I quoted, the relevant solutions of Einstein's equation describe universes that are either finite at all times or infinite at all times. And an open universe is by definition infinite.

Not really. It was an attempt to describe what GR says, but it didn't look anything like an attempt to describe what spacetime is. You need to realize that concepts like "spacetime", "energy", "photon", etc., are all defined by theories. "Spacetime" is defined by GR as a smooth manifold. That's a "proper characterization of what spacetime is".

Keep in mind that there is no "big bang event". The big bang is a property of a class of solutions of Einstein's equations. It's a name for what happens to certain variables when you let a parameter that can be interpreted as time go to zero.

"Preceded" refers to something at an earlier time, i.e events with a time coordinate t that's less than the time coordinate at the big bang. But the big bang doesn't have a time coordinate. It's a limit, not an event. Specifically, the limit t→0. And even if we pretend that the big bang is an event with t=0, how can something be earlier than that when t>0 at all events in spacetime?

This is not fancy talk to avoid the issue. You may feel intuitively that there must be an earlier time, but the experiments that have probed the accuracy of the predictions of GR have proved conclusively that our intuitive ideas about space and time are dead wrong.

You started with a philosophical question about something that the universities don't cover well, so there aren't many people here who can give you a good answer. Then you wrote a rather long (and wrong) description of GR that takes a lot of time to read and correct, and was more appropriate for the cosmology forum anyway. Also, it may not be the greatest idea to keep making more posts in a thread where you are the only one who have posted, because it looks like there's a discussion going on...until we open the thread of course, but I'm less likely to do that if I think someone else has already answered.

Last edited: Aug 27, 2009
11. Aug 27, 2009

### atyy

Just a bit more detail:

The EFE relates spacetime geometry and energy. To know how matter moves, one also needs (i) equation of state relating the various properties of the matter (ii) an equation relating the various properties of the matter and its energy. The joint solution to the EFE and the equations for matter gives you the properties of matter as a function of spacetime geometry, ie. how matter moves as a function of "time" in "space".

12. Aug 27, 2009

### atyy

13. Aug 27, 2009

### atyy

In general relativity, there are a bunch of effects that are "not real" in the sense that they are coordinate dependent (due to a particular way of dividing spacetime into "space" and "time"). There are also a bunch of effects that are "real" in the sense that they are coordinate independent. By using general relativity to define "not real" and "real", the expansion of "space" with "time" is actually "not real" - but that's ok - we just have to know that it's one of many ways of splitting spacetime into "space" and "time". For comparison and in contrast to the expansion of space with time, spacetime curvature is "real" in general relativity.

Also, "gravity" was actually first defined as something "real" by Newton's theory of gravity. According to GR, Newton's theory is not true, therefore according to GR, there is no such thing as "gravity" as defined by Newton's theory. But GR does model as spacetime curvature many of the same phenomena as Newtonian gravity, which is why we say, according to GR, "Newtonian gravity" is spacetime curvature.

If we had the true theory of everything, we could use it to make another definition of "real". Since we are pretty sure that general relativity is not the true theory of everything, we can pretty much say that general relativity is not "real", according to the true theory of everything.

Edit: From the point of view of the true theory of everything, general relativity is an "effective theory" effective in describing experimental observations in some regime; from the point of view of general relativity, Newton's theory is an "effective theory" describing experimental observations in an even smaller regime; from the point of view of Newton's theory, modelling the gravitational field of the earth as providing a constant acceleration of 9.8 m/ss is an "effective theory" effective in describing experimental observations such as a pendulum on your desk. For more about the viewpoint of effective theory http://www.people.fas.harvard.edu/~hgeorgi/review.pdf .

Last edited: Aug 27, 2009
14. Aug 27, 2009

### Fredrik

Staff Emeritus