# The Uncertainty Principle and Quantized Time

1. Oct 19, 2005

### Toptomcat

GIVEN:
1. The more accurately you determine a particle's position, the less you know about its momentum, and vice versa. (Heisenberg Uncertainty Principle)
2. Momentum is defined as mass times velocity.
3. Velocity is defined as change in position over time.
4. The rest mass of a particle is definite and non-probabalistic.
5. The increase in mass that occurs to a particle when its velocity increases is also definite and non-probabalistic.
6. Time is quantized- that is, it has a smallest possible unit of duration.
7. Space is also quantized, being time in different clothes. It has a smallest possible unit of length- possibly the Planck length.

Now, suppose you are measuring a the position of a particle of known rest mass as precisely as possible, as often as possible- that is, you are getting it to the nearest space quanta, once per time quanta.

You now have a list of positions, with precise times of occurence for each. You can derive the velocity of the particle, as precisely as is possible, by seeing how much its position changed between each measurement.

From its velocity you can infer its current mass, because you know its rest mass and can calculate how much it's increased from that from the velocity.

Now that you have its velocity and mass, it's a simple matter to calculate its momentum, being the product of the two.

I now have figures that cannot be more precise, for a particle's simultaneous velocity and position- in violation of the Uncertainty Principle.

Either there's a hole in my logic or one or more of my givens is wrong. The first five aren't really in question. Have I disproved the last two, or am I having delusions of grandeur?

2. Oct 19, 2005

### Danger

It would appear to me, if I understand your post correctly, that you are overlooking the fact that the act of measuring the position and/or energy alters them.

3. Oct 19, 2005

### Toptomcat

Yes, but you'll know by how much once you take the next measurement.

Unless the Uncertainty Principle is only meant to apply to the present, not the past...?

Last edited: Oct 19, 2005
4. Oct 19, 2005

### Danger

Exactly. You can know where it was, but it won't be there any more.

5. Oct 19, 2005

### Toptomcat

I see. So, just to be clear, you CAN know the exact position and momentum of a particle at a single point in the PAST, but NOT the present?

6. Oct 19, 2005

### Danger

I believe that's how it works. QM is not my greatest area of knowledge, though, so you'd best gather some other opinions.