Is there a minimal measurement of time?

[5614]

Although each time Einstein tried to disprove quantum mechanics (QM) he lost his argument, each "test" Einstein put QM through QM worked every time.

 

For calculating the Plank Time sometimes [math]h[/math] is used and sometimes [math]\hbar[/math] is used. This results in either a [math]\times 10^{-44}[/math] or [math]\times 10^{-43}[/math]. Respectable sites use a combination of both values... which one is correct? Why are [math]h[/math] and [math]\hbar[/math] seemingly interchangable?

[swansont]

But why? If gravity is safely neglected at atomic scales surely it can totaly neglected at Planck scales?

 

I know that is wrong' date=' because at that scale quantum effects (incl. quantum gravity) play major roles... but how can such a small force like gravity play any effect at such small levels?[/quote']

 

Gravity is neglected at our energy scales. But what of the early universe, when energy densities were much higher. Does the same statement apply?

[swansont]

For calculating the Plank Time sometimes [math]h[/math] is used and sometimes [math]\hbar[/math] is used. This results in either a [math]\times 10^{-44}[/math] or [math]\times 10^{-43}[/math]. Respectable sites use a combination of both values... which one is correct? Why are [math]h[/math] and [math]\hbar[/math'] seemingly interchangable?

 

Factors of two and pi are often neglected, or put in different parts of a formula. Conceptually it's often the order of magnitude that's important. h is really small.

 

If someone told you you had a temperature of 10 million degrees, how much would it matter if it were C or F?

[5614]

That's a good answer... but I don't like it!

 

So sure, both h and hbar are very small... but just freely interchanging between 2 different values in physics and saying they're both right and there's no real difference... they're different numbers, maybe like Newtonian motion it's hard to see when it might be wrong, but one must be right, making the other wrong.

 

[math]h \neq \hbar[/math] so pretending that they are and that you can switch between them at leisure.... just, do you know what I mean? It just don't sound right.

[swansont]

You have to be consistent, of course. It might depend on whether you prefer e.g. to determine the momentum of a photon as [math] h/\lambda[/math] or [math]\hbar k[/math]

[Ragib]

yea, it depends on which equations you choose to go by. h and hbar are not different numbers derived differently, hbar is just h divided by 2pi. They do this so other equations are simpler.

[5614]

I know that [math]\hbar = \frac{h}{2 \pi } [/math]

 

So if you said that [math]p_{photon} = h / \lambda[/math] could you say that [math]p = \hbar / \lambda[/math]?

 

I don't think you could but if you look somewhere like here:

http://scienceworld.wolfram.com/physics/PlanckTime.html

then it shows both h and hbar used in the same equation. Surely only one can give the right answer.

 

Actually, maybe they're not the same formula. One is for tp and the other for t'p.... what's the difference?

[Ragib]

Lol, you actually gave me a good example 5614. No, they arent the same equations, they are two exactly the same equations, except one is hbar and one is h. Once again, you choose which one you use in your calculations and then stick by that choice when using h or hbar again. If you change your choice in the middle of your calculations, you will get a wrong answer.

[Ragib]

In fact, it even says on the webpage, If h-bar is used instead of plain h, the corresponding time is...blah blah, you can choose which you use.

[Ragib]

And it also says, See also, planck mass, area, length, and on all those web pages, it says, if you use hbar instead of h.

[5614]

My point is that if you have a photon with frequency 'f' and you want to calculate it's energy then if you use h you get one value and if you use hbar you get a different answer. That photon has a specific energy, it cannot be one of two depending on how you feel. Only h gets you the right answer in that equation, using hbar yields an incorrect answer.

[Severian]

A quantization of time or space would cause a breaking of Lorentz invariance. Since Lorentz invariance has been tested extremely well by now, we know it is not broken up to roughly the Planck scale.

 

So if space is quantized, its indivisible unit is smaller than a Planck length 1.61624(12)x10^-35m.

[Ragib]

5614, yes you do get differnt values. Both are correct, hbar yeilds an answer in different units.

[Hikaru79]

Since the topic asks minimal measurement of time, then perhaps

 

[math]\Delta E\Delta t\geq\dfrac{h}{4\pi}[/math]

 

is appropriate?

 

EDIT: Oh, drat! I didn't realize there was a second page when I replied. And there's no "delete" button. Sorry! ^ ^: