Is Space-Time Continuous or Quantized?

[GregoryC]

TL;DR Summary

Feelings and or reactions...

A free photon can have any wavelength and energy; no discreteness there. Just because something is quantized, or fundamentally quantum in nature, doesn’t mean everything about it must be discrete.

The idea that space (or space and time, since they’re inextricably linked by Einstein’s theories of relativity) could be quantized goes way back to Heisenberg himself. Famous for the Uncertainty Principle, which fundamentally limits how precisely we can measure certain pairs of quantities (like position and momentum), Heisenberg realized that certain quantities diverged, or went to infinity, when you tried to calculate them in quantum field theory. Space and time are both continuous. It’s possible that the problems that we perceive now, on the other hand, aren’t insurmountable problems, but are rather artifacts of having an incomplete theory of the quantum Universe. It’s possible that space and time are really continuous backgrounds, and even though they’re quantum in nature, they cannot be broken up into fundamental units. It might be a foamy kind of spacetime, with large energy fluctuations on tiny scales, but there might not be a smallest scale. When we do successfully find a quantum theory of gravity, it may have a continuous-but-quantum fabric, after all. Taken from an article in Forbes by
I am a Ph.D. astrophysicist, author, and science communicator, who professes physics and astronomy at various colleges. I have won numerous awards for science writing…

 

[.Scott]

They are not "quantized" in the sense of there being only a countable number of "space units" or "time units".
But there is a lower limit on what is meaningfully discernible.
See: https://en.wikipedia.org/wiki/Planck_length

 

[PeterDonis]

there is a lower limit on what is meaningfully discernible

Actually we don't know that for sure. The hypothesis that the Planck length sets a lower bound on meaningful lengths (and times) is a speculative hypothesis. Many physicists think it is plausible, but we have no evidence either way (since the Planck scale is many orders of magnitude smaller than the smallest scale we can currently probe experimentally).

 

[GregoryC]

Actually we don't know that for sure. The hypothesis that the Planck length sets a lower bound on meaningful lengths (and times) is a speculative hypothesis. Many physicists think it is plausible, but we have no evidence either way (since the Planck scale is many orders of magnitude smaller than the smallest scale we can currently probe experimentally).

I read that the energy we would need to probe these small scales is about the energy density of the universe. And if Kurt Godell is right we will never be able to totally understand our universe because we cannot observe it from the outside.

 

[PeterDonis]

I read that the energy we would need to probe these small scales is about the energy density of the universe.

I'm not sure what you mean by "the energy density of the universe". The average energy density of the universe is tiny, about $10^{-29}$ grams per cubic centimeter.

The Planck energy is the energy that would be needed to probe the Planck scale of length and time. It's not an energy density, it's an energy per particle, like the energies quoted for accelerators like the LHC. The Planck energy is about $10^{19}$ GeV, or about 15 orders of magnitude larger than the LHC energy.

 

[GregoryC]

I miss stated my thought. I meant to say it would take the energy contained in all the universe to see those details. That still does not change the incompleteness theorem. Unless we can view the whole of any system we can never know everything about the system. We are as Sabine says "LOST IN MATH"...

 

[PeterDonis]

I meant to say it would take the energy contained in all the universe to see those details.

I take it you mean all the energy in the observable universe. That's still way, way off, since the Planck energy, while very large in terms of energy for a single particle, is a small amount of energy in ordinary terms--it's the equivalent of about $10^{-5}$ grams of mass.

That still does not change the incompleteness theorem.

Godel's Incompleteness Theorem doesn't say anything about physics. It's about math.

 

[GregoryC]

I take it you mean all the energy in the observable universe. That's still way, way off, since the Planck energy, while very large in terms of energy for a single particle, is a small amount of energy in ordinary terms--it's the equivalent of about $10^{-5}$ grams of mass.
Godel's Incompleteness Theorem doesn't say anything about physics. It's about math.

Lee Smolin just thinks he discovered a way to disprove Godels theory. Just today. Have not had time to read yet. More to come when I finish reading it.

 

[PeterDonis]

Lee Smolin just thinks he discovered a way to disprove Godels theory.

Do you have a reference?

 

[GregoryC]

Do you have a reference?

https://www.quantamagazine.org/were...MxD6dt70Zuw7qm7RSFSjeXNQ3FB_Z-B32kQ52LK1IqQgw

 

[PeterDonis]

@GregoryC, the reference you give is a pop science article. It's interesting, but not a valid basis for PF discussion.

The OP question has been answered, so this thread is closed.