Is Space and Time Really Continuous or Discrete?

[Naty1]

Mijfin:

I've always thought of this space as being empty, without any mass in it- basically as nothingness. So my question is, what is it that allows spacetime to curve like this?

The experts are currently off on a tangent, so maybe a novice can provide some insights. Nobody has a definitive answer. Short answer: Spacetime is NOT nothingness, it is not 'empty', but what it is is unclear.

It is not 'absolute and fixed' [special relativity], it curves [general relativity] it has quantum fluctuations, energy density, {quantum mechanics] horizons, and seems to evolve [cosmology], it sets the characteristics of all particles [string theory]. So in some 'real' sense what you see depends on what you ask.

Nobody knows exactly what space...nor time are. Nor the exact relationship between them. Relativity says they are interchangeable and depend on the observer. Scientists often disagree on some characteristics ofspace ...is it continous, or discrete, or are those questions not even relevant? Disagreements remain: relativity suggests continuous, quantum theory, discrete.

What we do understand is that gravity is reasonably well explained by attributing curvature to space and time. We can explain most experimental observations using that description. But is is likely not the final resolution because it conflicts with quantum mechanics, also an outstanding theory, when radical curvatures exist...singularities...neither theory works the way we would like.

Also, local space is not exactly the same as distant space: In some snese particles have a clear unambiguous local description [they are what you measure] but trying to define them in curved spacetime is mathematically difficult. But even locally, an accelerating and an inertial observer will record different temperatures of 'empty space'...

Here is a quote I kept from a discussion in these forums...from a higly regard classic textbook [Miller, Thorne, Wheeler]:

...nowhere has a precise definition of the term “gravitational field” been
given --- nor will one be given. Many different mathematical entities are
associated with gravitation; the metric, the Riemann curvature tensor, the
curvature scalar … Each of these plays an important role in gravitation
theory, and none is so much more central than the others that it deserves the name “gravitational field.”

So what the authors say is 'we can't even associate gravitational curvature with a single, exact, precise mathematical term'...there are multiple aspects to curvature.

Here is a current forum discussion from the perspective of thermodynamics: space and gravity are essentially degrees of freedom. While the issue here is "what is gravity, really?" it relies on the statement below which is relevant to your question.

Emergent Gravity
https://www.physicsforums.com/showthread.php?p=3984153#post3984153

from the referenced paper:

...In the second part, I describe a novel way of studying cosmology in which I interpret the expansion of the universe as equivalent to the emergence of space itself. In such an approach, the dynamics evolves towards a state of holographic equipartition, characterized by the equality of number of bulk and surface degrees of freedom in a region bounded by the Hubble radius.

Others [experts] in these forums rail against such a view and insist space is NOT expanding: that cosmological expansion is NOT really a physical manifestation of expanding space and claim it is a mathematical artifact...called the metric.

So adopt your own point of view and test it against different perspectives and theories. Remain open minded.

 

[PeterDonis]

I don't know if it is a general attitude, but that accurately reflects my attitude.

I read the Geroch quote that bobc2 brought up a while back as expressing a similar attitude.

 

[PeterDonis]

So what the authors say is 'we can't even associate gravitational curvature with a single, exact, precise mathematical term'...there are multiple aspects to curvature.

No, they said we can't associate the gravitational field with a single mathematical object. Curvature can be associated with a single mathematical object: the Riemann curvature tensor. But "gravity" itself or the "gravitational field" is more than just spacetime curvature; it's all the things we associate with gravity.

I think the best answer to the OP's question was given in post #3 by DaleSpam.

 

[PeterDonis]

from a higly regard classic textbook [Miller, Thorne, Wheeler]

Oh, btw, it's Misner, Thorne & Wheeler.

 

[Dale]

Disagreements remain: relativity suggests continuous, quantum theory, discrete.

Space and time are continuous in modern quantum mechanics (QED, QFT, standard model).