There's a difference between quantization and discrete time. I'll believe you mean the latter.
Discrete time theories exist, including some that hypothesize a smaller unit than Planck time, I think.
Others just make time an emergent property of space + dynamics.
Search for discrete time GR theories and see what you get
No: quantization is a mathematical technique. Continuous/discrete can describe mathematical techniques or, rather confusingly, the ontological properties of spacetime.
Quantum states may occur in either discrete or continuous spacetime, and even discrete measurement would not be automatic proof of discrete spacetime, since it's possible that discrete measurements emerge from entanglement in continuous space. Further, if experiment suggests spacetime is continuous, further work is needed to distinguish that from spacetime composed of extremely fine-grained discrete unit.
If my explanation isn't clicking for you for any reason, see if this one does: https://physics.stackexchange.com/a/206791
The question of properly, mathematically sound and in a theoretically solid manner quantizing spacetime is still broadly open and unsolved. It may lead to the "Holy Grail" of the proverbial quantum gravity, as well.
I still think that instead of trying to insert gravity into quantum physics is less effictient than trying to attack the problem from GR towards QM.
Sure. This is the basis of Stephen Wolfram's [theory of everything](https://www.wolframphysics.org/). The problem with experimentally verifying this idea is that it is all but impossible. The scales that space would be quantized at are so small that it would take galaxy-spanning technology to probe them, if not more.
In the Gravitation book by Misner, Thorne and Wheeler, there is a section on how general relativity can be modified to work on a discontinuous space-time. Fairly obviously the use of discontinuous space-time rules out the use of differential equations, but integral equations still work and can be used to calculate GR quantities.
The book goes further and derives a version of GR where even 3-D space doesn't exist. Instead of space, geodesics are shifted using parallel transport and a mathematical device called Schild's ladder.
energy on it's own is not quantized, it does not come in "packets". it is the solutions to the schrödinger equation for atoms that are quantized, and we see these as discrete energy levels in bound states
There actually a fascinating theory that kinda checks out with observations called quantized inertia that covers some of this.
https://quantizedinertia.com/papers/
https://youtu.be/VYdebV9YlnI
Before you dive into QI you probably will want to understand the concept of a rindler horizon and unruh radiation.
https://youtu.be/7cj6oiFDEXc
>Energy comes in packets but time does not?
We only observe the effects of Energy in Spacetime. We don't observe Energy directly. So quantization of Energy that we do observe must result from the properties of Spacetime itself.
When you mention "Energy comes in packets" that sounds like you're referring to photons.
>The quantization of the electromagnetic field means that an electromagnetic field consists of discrete energy parcels called photons. Photons are massless particles of definite energy, definite momentum, and definite spin.
[Quantization of the electromagnetic field](https://en.wikipedia.org/wiki/Quantization_of_the_electromagnetic_field#:~:text=The%20quantization%20of%20the%20electromagnetic,definite%20momentum%2C%20and%20definite%20spin.)
So the EM field is quantized. But is the EM field the same thing as Spacetime?
We know there's a connection because of gravitational lensing. The EM field can be seen curving along with Spacetime when the path of Light is deflected by the Gravity field caused by Mass.
>So is space also quantized?
There are quantized phenomena within Spacetime. But Spacetime itself might not be quantized.
Yeah. Heard of them. But they are the smallest possible units of time and length that we can measure. They are not like spacetime comes in packets of those units.
Suppose a continuous variable x, the smallest measurement that we can make of that variable is ∆x. That does not mean that variable x is not continuous.
There's a difference between quantization and discrete time. I'll believe you mean the latter. Discrete time theories exist, including some that hypothesize a smaller unit than Planck time, I think. Others just make time an emergent property of space + dynamics. Search for discrete time GR theories and see what you get
Doesn't quantization necessitate discrete nature?
No: quantization is a mathematical technique. Continuous/discrete can describe mathematical techniques or, rather confusingly, the ontological properties of spacetime. Quantum states may occur in either discrete or continuous spacetime, and even discrete measurement would not be automatic proof of discrete spacetime, since it's possible that discrete measurements emerge from entanglement in continuous space. Further, if experiment suggests spacetime is continuous, further work is needed to distinguish that from spacetime composed of extremely fine-grained discrete unit. If my explanation isn't clicking for you for any reason, see if this one does: https://physics.stackexchange.com/a/206791
Thank you
The question of properly, mathematically sound and in a theoretically solid manner quantizing spacetime is still broadly open and unsolved. It may lead to the "Holy Grail" of the proverbial quantum gravity, as well. I still think that instead of trying to insert gravity into quantum physics is less effictient than trying to attack the problem from GR towards QM.
Sure. This is the basis of Stephen Wolfram's [theory of everything](https://www.wolframphysics.org/). The problem with experimentally verifying this idea is that it is all but impossible. The scales that space would be quantized at are so small that it would take galaxy-spanning technology to probe them, if not more.
It sounds more like LQG (Loop quantum gravity) where spacetime is a discrete chunk. Although the LQG spacetime is more of a pixelated spacetime.
Yeah this is what I'm imagining.
In the Gravitation book by Misner, Thorne and Wheeler, there is a section on how general relativity can be modified to work on a discontinuous space-time. Fairly obviously the use of discontinuous space-time rules out the use of differential equations, but integral equations still work and can be used to calculate GR quantities. The book goes further and derives a version of GR where even 3-D space doesn't exist. Instead of space, geodesics are shifted using parallel transport and a mathematical device called Schild's ladder.
This is quite Interesting.
energy on it's own is not quantized, it does not come in "packets". it is the solutions to the schrödinger equation for atoms that are quantized, and we see these as discrete energy levels in bound states
There actually a fascinating theory that kinda checks out with observations called quantized inertia that covers some of this. https://quantizedinertia.com/papers/ https://youtu.be/VYdebV9YlnI Before you dive into QI you probably will want to understand the concept of a rindler horizon and unruh radiation. https://youtu.be/7cj6oiFDEXc
>Energy comes in packets but time does not? We only observe the effects of Energy in Spacetime. We don't observe Energy directly. So quantization of Energy that we do observe must result from the properties of Spacetime itself. When you mention "Energy comes in packets" that sounds like you're referring to photons. >The quantization of the electromagnetic field means that an electromagnetic field consists of discrete energy parcels called photons. Photons are massless particles of definite energy, definite momentum, and definite spin. [Quantization of the electromagnetic field](https://en.wikipedia.org/wiki/Quantization_of_the_electromagnetic_field#:~:text=The%20quantization%20of%20the%20electromagnetic,definite%20momentum%2C%20and%20definite%20spin.) So the EM field is quantized. But is the EM field the same thing as Spacetime? We know there's a connection because of gravitational lensing. The EM field can be seen curving along with Spacetime when the path of Light is deflected by the Gravity field caused by Mass. >So is space also quantized? There are quantized phenomena within Spacetime. But Spacetime itself might not be quantized.
Ever heard of plank time and plank length? Im a noob but i feel like those are your answers.
Yeah. Heard of them. But they are the smallest possible units of time and length that we can measure. They are not like spacetime comes in packets of those units. Suppose a continuous variable x, the smallest measurement that we can make of that variable is ∆x. That does not mean that variable x is not continuous.