# Are points of spacetime unique?

1. Sep 30, 2011

### Runner 1

Are any known laws of physics a function of a unique spacetime coordinate?

Be careful reading my question -- I'm not asking if the laws of physics vary throughout spacetime (since they don't).

2. Oct 1, 2011

Staff Emeritus
I don't think you wrote what you meant to write. There are no unique coordinates - New York may have a position of 0,0 in a coordinate system centered on New York, and a different position in a coordinate system centered on London.

3. Oct 1, 2011

### haael

Are you asking if there is a physical field that is a bijection from spacetime coordinates to, say, complex numbers? There is no such physical (measurable, observable) field. All fields corresponding to measurable quantities are smooth functions of coordinates and there are no smooth bijections to complex numbers from a Cartesian coordinates of a dimension greater than 2.

But you can of course define some abstract non-smooth bijection of coordinates, that may have some application in physics.

4. Oct 1, 2011

### pb09203009

the water boiled on a mountain would be easier than water boiled at the see level.
and it would also be easier in the day than the night.

this is a simple example of "a function of a unique spacetime "

but as we study further, we will unify these differences.

so, the aim of physics is to understand "unique" as unification

5. Oct 1, 2011

### Runner 1

haael, I'm not quite at that level of math in physics, so I can't really say. It might answer my question...

(pb09203009, did you really register an account just to say that?)

I'll try to give an example.

Basically, the wavefunction for any particle's state "collapses" upon measurement into a value that can only predicted statistically. An identically prepared state gives different measurements each time one is taken.

My question though -- the experiments aren't "really" identical. One may be performed at 12:05 PM and the other at 12:20 PM. A different amount of time has elapsed since the universe began. Not to mention that it's impossible to get one particle into the same exact position that it once was (HUP limits these sort of things). Is it possible that something deeper below Planck scale is taking place that is dependent on the time since the universe began? I.e., the electron's measurement will depend on f(t), where t is the time since the universe began. Except that we can't find what f(t) is because of HUP.

So imagine you position identical electrons with identically prepared states in a 3D lattice in space with equal spacing. And suppose you could take a measurement at the same time for all of these electrons. The data for each individual measurement is unpredictable. Is it possible that if you analyzed the data from all of the measurements together you would find a correlation? (That's not to say you would -- this is just an example).

In other words, it's sort of a spacetime analogy to indistinguishable electrons. If you assume electrons are not unique, then you get statistics that correctly predict their behavior. If you assume they are unique, then you get statistics that don't fit any experiments so far.

My question -- is each point in spacetime indistinguishable? And if so, why? I'm not looking for the "laws of physics are the same in all reference frames", because that doesn't answer the question. The laws are of course the same everywhere, but theoretically could be a function of a unique spacetime coordinate (unless someone's already proven why this isn't the case).

6. Oct 1, 2011

Staff Emeritus
These fall into a category of theories called "hidden variable theories", and it has been shown by John Bell that such theories do not give the same predictions as quantum mechanics.

7. Oct 1, 2011

### Runner 1

Okay, thank you. I'm surprised my idea had a name. Reading the Wikipedia article on it now...

8. Oct 1, 2011

### Runner 1

Roughly what percentage of (non-crackpot) physicists believe in a hidden variable theory?

9. Oct 2, 2011

Staff Emeritus
Non-crackpot? 0%

10. Oct 2, 2011

### fleem

True of local hidden variable theories. Non-local hidden variable theories (i.e. "everything is entangled", Mach's principle realized, etc.) can be created to explain pretty much anything.

11. Oct 2, 2011

Staff Emeritus

12. Oct 2, 2011

### ThomasT

I don't understand your question. Do you mean something like: are the laws of physics unique to the universal evolutionary epoch in which they're discovered? That is, might the laws of physics be different, say, a trillion years from now, or is it possible that they were different in the distant past? That is, is it possible that the laws of physics are evolving as the universe evolves?

13. Oct 2, 2011

### friend

If one point in space is indistinguishable from another point in spacetime, then wouldn't that mean that you could get to New York by going to L.A. Or you might be able to get to the past at a certain point in the future.

14. Oct 2, 2011

### haael

De Broglie-Bohm interpretation is a hidden variable theory and quite a few percent of physicists believe in it to some degree.

15. Oct 2, 2011

### ThomasT

Wouldn't this be due to the fact that the universe is evolving, rather than due to the HUP?

That's sort of how I was framing your question in my previous post. I don't know if that question is answerable.

Is it possible that the evolution of the universe is governed by fundamental dynamics that remain the same as the universe evolves?

During humanity's expected short existence I wouldn't suppose that we'd see any changes in physical laws depending on t. Again, I don't see our inability to find f(t) as being due to HUP. Rather, we just don't have any direct physical apprehension of any spacetime epoch other than the one we happen to be evolving in. We can extrapolate and project, but that's based on the laws of physics as they've been formulated during our particular interval of existence.

I think that, sure, in that case, you would find a correlation. If that experiment could be done. But it can't.

Electrons are identical in the sense that they're defined in terms of certain attributes or properties. But the electrons that are moving in my computer aren't the same electrons that are moving in your computer, even though we couldn't differentiate one of your electrons from one of my electrons if we were able to put them side by side and compare them.

No. They're distinguishable. Spacetime point (x,y,z,t) is distinguishable from spacetime point (x',y',z',t').

As Vanadium 50 said, you can center your spacetime grid arbitrarily. But no matter where you might choose to center it, each spacetime point refers to a unique location in spacetime.

Why "of course"? All we know is that wrt our very limited perspective during our exceedingly short existence our current formulation of the 'laws of physics' seems to hold. But there's still no understanding of things in terms of a fundamental dynamical principle or law.

I still only understand what you're saying in connection with what I've conjectured that it might mean.

Also, I don't understand what this might have to do with the impossibility of formulating local realistic hidden variable models of quantum entanglement per Bell.

16. Oct 2, 2011

### Runner 1

Yeah, I meant that it's impossible to get two things in the same spacetime coordinate. Although I suppose you could do that with bosons...

I was kind of meaning is it possible that the laws follow an f(t) form. There's so many theorems out there prohibiting certain physics ideas from being true, so I didn't know if this one was prohibited.

They're different only to a point though. From the Wikipedia article on "Identical particles", "Even if the particles have equivalent physical properties, there remains a second method for distinguishing between particles, which is to track the trajectory of each particle. As long as we can measure the position of each particle with infinite precision (even when the particles collide), there would be no ambiguity about which particle is which. The problem with this approach is that it contradicts the principles of quantum mechanics."

I thought if I made the suggestion that the laws of physics don't hold, I'd get labeled a crank :P