Discontinuity of Spacetime (and other things)

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We know that matter is discrete, and energy is quantized, (and more quantized things I don't know about.) There is also Planck length? and Planck time?

Is spacetime continuous?
If we don't know yet, I sure hope it is, because I much prefer to imagine discrete matter and energy interacting in a continuous "environment."

What implications would there be if spacetime was not continuous?

I, for some reason, really hope that spacetime is continuous.

Then again, I also think that whatever is the real case, perhaps it would be possible to model spacetime to be continuous and not care about what it really is, as long as it explains phenomenon and can be used to engineer things.

Oh, one more thing: What is the deal with string theory? Why has it been a candidate for a theory of everything for so long? What are string theorists working on at the moment? What does string theory have to say about spacetime, (other than it's dimensions, for example, it's continuity.)?
 

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Is spacetime continuous?
If we don't know yet, I sure hope it is, because I much prefer to imagine discrete matter and energy interacting in a continuous "environment."
I'm not a scientist, but I think the theory for determining whether spacetime is continuous or not is called 'quantum gravity'. Its goal is to quantize space, from what I understand. That would mean spacetime consists of discrete chunks and is not continuous.

I personally don't believe that there is a totally continuous environment at any order of magnitude below what we can currently probe.
 
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Hmm, well if spacetime is quantized, does that mean that a locational probability distribution (in quantum mechanics) for a particle in a closed region would only contain a finite number of possible "locations" rather than a continuous cloud of probability?

Wouldn't that also make the "spacetime continuum" a misnomer?
 
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DaveC426913
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What implications would there be if spacetime was not continuous?

I, for some reason, really hope that spacetime is continuous.

Then again, I also think that whatever is the real case, perhaps it would be possible to model spacetime to be continuous and not care about what it really is, as long as it explains phenomenon and can be used to engineer things.
This is one of the biggest mysteries of our time: the incompatibility between our two major theories: GR and QM. For GR, spacetime must be continuous; for QM, it must be discrete. When you try to reconcile them, you get non-sensical answers.
 
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This is one of the biggest mysteries of our time: the incompatibility between our two major theories: GR and QM.
By any chance, do you (or anyone else) know how string theory is coming along? I know it is a candidate for a theory of everything, but what are it's current obstacles?
 
  • #6
DaveC426913
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By any chance, do you (or anyone else) know how string theory is coming along? I know it is a candidate for a theory of everything, but what are it's current obstacles?
Last I heard (and it's been a while),
1] string theory allows so many possibilities (virtually countless) for the configuration of the universe that it doesn't explain why this is the one we got.
2] It doesn't predict anything testable, which is another way of saying it is not falsifiable, which is another way of saying it's not scientifically valid.

...and a quick peek at the Wiki entry for it suggests these are still problems.
 
  • #7
DrGreg
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I've only ever paddled in shallow waters of quantum theory, but the impression I have is that although some things are discrete, like the energy levels of an atom, or the decomposition of matter and electromagnetic radiation into discrete particles, there are lots of other things that aren't discrete. For example, the location of a free electron in empty space may be uncertain, but the possible locations form a continuum. (People who say that all distances are an integer multiple of a Planck length have, I believe, misunderstood the concept -- that would be incompatible with relativity anyway.)

That's my impression of our current understanding, but as we don't yet have a successful merger of GR and quantum theory, who knows what that might turn up?
 

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