Kruzkal

What things are discrete in the universe? And what things are continuous?

Energy in a sense is discrete when you get to a small enough value i.e. the charge of an electron, photon, etc. Mass (a from of energy) when you get to a small enough value i.e. to atomic mass of particles, protons also seems to be discrete. What do you peeps think? What about measurements of dimentions like time and distance?

I would like to know what others think in terms of the whether the universe is discrete, continuous, a bit of both, or neither?

Thanx in advance . . .

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The answer to the ultimate question of life, the universe, and everything is 42

spacer1

Hi Kruzkal,

I think that if we take the expansion of the universe as continuous, then we must assume that everything is continuous and in constant motion. The notion of discrete, then, is only a mental construct (arresting of continual motion).

NialScorva

It's both.

nermal

Did you deliberately wait for that post number to ask such a question? Just curious.

Ed

eh

Energy is discrete, and the notion of discrete space seems to be popular in physics. In Loop Quantum Gravity, for example, area and volume only come in discrete sizes, though I'm not sure that's the case for length.

Kruzkal

I made that post before it was 42 actually, it just happens to be 42 when you looked at it. I used that sig in many other posts of mine before.

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ohwilleke

I'd say that we don't know.

Newtonian mechanics are premised on a continuous universe, and both general and special relativity are also theories that presume continuity.

Quantum mechanics, of course, looks at the universe in more of a discrete way, assuming that matter and energy come in discrete quanta.

A number of theories propose a minimum quantized distance of 10^-33 meters or so, but there is really nothing empirical to back it up. The fact that the Feynmann equations aren't scalable to an infinitely small level without quite a bit of mathematical legdermain, is probably the best empirical evidence in favor of this theory.

Quantum Ninja

Here's an idea:

If energy is discrete, then does that mean that mass, distance, and time must necessarily be discrete, too? The basic unit of energy is the Joule (kg*m^2/s^2). If Joules come only in discrete values, and a Joule is really just a combination of three simpler measurements, then wouldn't those measurements also have to be discrete?

For instance, if the energy of a photon is equal to its frequency multiplied by Planck's constant, and energy is discrete, then doesn't that imply that frequency must also be discrete? Compare, for example, a photon that posesses the smallest possible energy value (we'll call it e1) and a photon that possess the next possible energy value (e2). Each of these photons have a unique frequency (f1 and f2, respectively). If frequency is continuous, what happens when you have a third photon with frequency f3 that is between f1 and f2? It can't have a unique energy level because there is no energy level between e1 and e2. It's like trying to find an integer between 1 and 2. It doesn't exist. So can we conclude that there is no f3 between f1 and f2, implying that frequency is also discrete?

The only work-around for this that I can think of is if the relationship between the two variables followed something like the floor function:



In the graph above, you can see that the set of values that X can take on is continuous, while the set of values that Y can take on is discrete. Does nature do something similar to this? Does nature "round down" or truncate to the nearest energy level?

the_cave

Hm, well, while we're calculating, units like "frequency" are just numbers; but it seems to me that when we're done, sure, one could say that units come in "discrete" amounts.

I don't want to sidetrack the topic, but I just wanted to add that for me, the biggest mystery was how there could be bottom units of things like time. I mean, if a unit of Planck time is the smallest that time gets, how do you know? I mean, I know the results are mathematical, but...what would you measure a unit of Planck time against to see how long it was? If you see what I mean. I realize some reasearch would be in order for me to answer this question, I just thought I'd throw it out there.

pmurray

My underdtanding was that action (energy * time) is discrete, and its unit is planck's constant.

As for space and time, there are various "quantum foam" ideas around.