# Size of universe and uncertainty principle

1. Jun 6, 2004

### kurious

If I use E x t = h bar

and put t = age of universe in seconds = 10^ 18 seconds,
E x 10^18 = 10 ^ -34 gives E = 10^ -52 Joules.

So if an oscillator of some sort in the early universe absorbed a photon,
and emitted the energy of that photon today, there would be an uncertainty in the photon energy of 10 ^ -52 Joules.This energy corresponds to a wavelength of 10 ^ 26 metres - the current size of the universe.
This makes sense because a particle can't exist outside of the universe -
the maximum uncertainty in its position has to equal the size of the universe.
So can the uncertainty principle be used to measure the size of the universe?

2. Jun 6, 2004

### chroot

Staff Emeritus
The uncertainty relation is not an equality, it's an inequality. What you described is the minimum possible uncertainty, but the real uncertainty could be much larger.

- Warren

3. Jun 6, 2004

### kurious

The uncertainty relation is not an equality, it's an inequality. What you described is the minimum possible uncertainty, but the real uncertainty could be much larger.

- Warren

But will this minimum uncertainty always relate to the real size of the universe?

4. Jun 6, 2004

### chroot

Staff Emeritus
No.

- Warren

5. Jun 6, 2004

### kurious

Why won't the minimum uncertainty always relate to the size of the universe?

6. Jun 6, 2004

### chroot

Staff Emeritus
Why would it? As I've already explained, the minimum uncertainty is a minimum. Nothing is stopping the uncertainty from being much, much larger. There's no reason to expect the universe to be at such a minimum.

Sorry, your argument about the size of the universe from an observation of the energy-time uncertainty relation is just not meaningful.

- Warren

7. Jun 7, 2004

### Chronos

i do agree that the size of the universe could never be zero or infinity. the uncertainty principle would forbid both states [an h-bar thing]. doing the math is, however, hard. that does, of course, assume the universe, as a whole, submits to quantum theory. i think it does, but, i have been wrong before.

8. Jun 7, 2004

### kurious

Sorry, your argument about the size of the universe from an observation of the energy-time uncertainty relation is just not meaningful.

The argument is meaningful if the oscillator is made from two particles which were at opposite ends of the universe at the time of the Big Bang - when the energy was absorbed by the oscillator ( this energy does not have to be a photon , it could be energy arising from the expansion of space-time, and when it is emitted, this could amount just to saying that the universe has contracted again), and assuming the universe oscillates over a time span of at least its current age, 10^18 seconds.Under all these conditions, the size of the universe at a particular time relates to the minimum uncertainty in the oscillator's energy, and, as you correctly say, not to the uncertainty in the energy the oscillator emits.

Last edited: Jun 7, 2004