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I have been thinking about the unification of general relativity and quantum mechanics. after giving it much thought I'm wondering if the problem is not in the formulas used but the numbering system. meaning we use a base ten system that can give an infinite number of values including zero. What if in the physical world there is no such thing as zero even empty space has energy. what if we used more like a digital based system not one and zeros but a discrete based system for instance for units of distance we used steps of the Planck length and for units of time we use the Planck's time? To me this would seem to eliminate infinity's because you could never have zero distance or zero time. I'm asking if it would be possible to incorporate these formulas in to GR and QM (D=D+ Planck's length) D minimum would be 1 Planck's length. (T=T+ Planck's time) T minimum would be 1 Planck's time.

Any thoughts?

I used Planck's Length and time as examples of discrete units. They may not be the values needed but the concepts is a discrete numbering system.

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closed as off-topic by HDE 226868, CR Drost, user81619, user10851, ACuriousMind Sep 6 '15 at 22:23

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It sounds as though you're asking why General Relativity can't be quantized. In other words, why can't General Relativity be used to predict accurate trajectories for objects as tiny as the planck length?

You suggested that the number system be changed so that the Planck length is the smallest digit. In order to do this, you'd have to presume that space itself comes in quantized volumes of about diameter 10^-35. This hypothesis has been experimentally falsified (see Lubos Motl's answer in the first link that Qmechanic listed in his comment to your question).

The problem with your suggestion is that at the Planck scale, quantum effects become important. Bits of the world at the Planck scale do not behave the same as macro objects such as trees, planets, and stars.

Both the position and the velocity of a particle at Planck scale can't be simultaneously determined. If you determine the position, the photon you use to see the particle will change it's velocity. Likewise, the photons you use to measure the particle's velocity will change its trajectory and position. In order for the world to be composed of quanta, each quantum must be "observed" by other quanta and/or aggregates of quanta. At the Planck scale the uncertainty principle prevents deterministic methods such as General Relativity from being used.

GR and QM are each experimentally successful in making predictions, but when quantum effects become important, GR is insufficient, and General Relativity and Quantum Mechanics are incompatible. Changing the number system will not solve the problem.

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  • $\begingroup$ Ernie I'm suggesting that space is quantized at some scale maybe not at the planks scale but smaller by several orders of magnitude. If it where that small even the Planck scale would seem macro . I do have ideas of how to derive these scales bases on physical measurements . I would love to have an open discussion if anyone is interested $\endgroup$ – newguy Sep 6 '15 at 17:48
  • $\begingroup$ Any unit at Planck scale or less runs into the problem of quantum effects. I should have made it more clear that the problem is not the scale of numbers, but the non-deterministic nature of the universe below that scale. Classical mechanics is deterministic, while QM is not. For alternative views, see this link: plato.stanford.edu/entries/determinism-causal/#QuaMec. Scroll down to sections 4.3 and 4.4. Unfortunately I think it's philosophy, not physics, so I don't know how much credence to give it. There's plenty of food for thought there, but I don't have time to explore it now. $\endgroup$ – Ernie Sep 6 '15 at 18:06
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You might find this article intresting, there is a non zero scalar component to the vacuum and a fundamental wavelength on the order of 10e-32 derived from plank's constant. Also an extra dimension.

Kaluza–Klein theory

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