Even if we switch to all renewable energy sources, like solar, wind, and hydroelectric power, carbon emissions would persist.
This is because carbon emissions largely come from oxygen reacting with carbon-containing molecules, which includes fossil fuel combustion, burning wood, plant and animal respiration, as well as organic decay.
Carbon is a fundamental building block of life and is present in nearly everything, from the food we eat to the materials we use. Complete elimination of carbon emissions would disrupt the carbon cycle and the basis of life itself.
There is a direct relationship between technology, the population size of biological species, the carbon cycle, and carbon emissions. Without some serious materials engineering sorcery to create materials from non-carbon resources, reducing carbon emissions too much would lead to population contraction and death. Renewable energy and financial growth are not proxies for material production.