λ

[ydoaPs]

how do you find the wavelength of a "big" object such as a person or a planet?

[ydoaPs]

if it's [imath]\lambda=\frac{h}{\rho}[/imath], then would you be able to use p=mv?

[DQW]

Crudely speaking, that is correct.

[Yggdrasil]

As long as your object isn't moving at near the speed of light (i.e. less than 10% of the speed of light), you can approximate its momentum to be mv.

[ydoaPs]

i calculated my wavelength when wlaking across a room and it is pretty close to the plank lenth. that makes me think that the earth's wavelength will be smaller. that doesn't make sense. doesn't length have pretty much no meaning under the plank length?

[timo]

I´ve never understood those "nothing has a meaning above/below the planck <add unit here>"-statements so far - but the only place I´ve encoutered them is in this forum, anyways. To my knowledge the Planck mass is just the energy (yes, I use c=1) where gravitation is estimated to be rougly as strong as the other forces. I´d bet you get the Planck length by multiplying suitable exponents of c and hbar so that the dimension fits. I do not know why this should lead to a statement as "length has no meaning below the Planck length".

But I am almost sure that earth´s gravity cannot be neglected.

[ydoaPs]

iirc, it has to do with uncertainty and warping of spacetime. i saw it on nova's the elegant universe. iirc, it was in the book as well.

[ydoaPs]

http://www.pbs.org/wgbh/nova/elegant/program.html

[timo]

Thx for the link. I think I´ll take a look at the streams when I have the time. Do you know which of the episode the statement is in?

Yes, it most certainly has to do with warping of spacetime. As a matter of fact, "gravity becomes strong" simply states that you can´t neglect spacetime warping anymore. I just don´t get the step to "therefore length becomes meaningless".

Can´t really see what it would have to do with uncertainty. But on the other hand, uncertainty in position might need a better definition in a warped spacetime. Perhaps that´s where it stems from.

[ydoaPs]

hour 2 chapter 1

[timo]

Watched it but didn´t find any statement on the Planck Length at all. Cool special effects, though.

 

But to come back to my original point: The reason why you end up below the Planck Length is probably because you´re dealing with a mass that has non-neglectible mass when it comes to gravity (whatever neglectible is supposed to be in the macroscopic regime) .

[ydoaPs]

at the end, "left and right...front and back...before and after..." it was worded differently in the book, but you get the idea.

[timo]

No, I don´t get the context with the Planck Length. I don´t even understand what that "left and right, ... lose their meaning" is supposed to say.

[ydoaPs]

John Wheeler coined the term 'quantum foam' to describe the frenzy revealed by such an ultramicroscopic examination of space (and time)---it describes an unfamiliar arena o fthe universe in which the conventional notions of left and right, back and forth, up and down (and even before and after) lose thier meaning. It is on such short distance scales that we encounter the fundamental incompatibility between general relativity and quantum mechanics. The notion of a smooth spatial geometry, the central principle of general relativity, is destroyed by the violent fluctuations of the quantum world on short distance scales. On ultramicroscopic scales, the central feature of quantum mechanics-the uncertainty principle-is in direct conflict with the central freature of general relativity-the smooth geometrical model of space(and of spacetime).

 

In practice, this conflict rears its head in a very concrete manner. Calculations that merge the equations of general relativity and those of quantum mechanics typically yield one and the same answer: infinity. Like a sharp rap on the wrist from an old-time schoolteacher, an infinite answer is nature's way of telling us that we are doing something that is quite wrong.⁶ The equations of general relativity cannot handle the roiling frenzy of the quantum foam.

 

The smallness of Plank's constant-whichgoverns the strength of quantum effects-and the intrinsic weakness of the gravitational force team up to yield a result called the Plank length, whichis small almost beyond imagination: a millionth of a billionth of a billionth of a billionth of a centimeter (10^-33centemeter).^{7[/sup'] THe fifth levil in Figure 5.1 thus schematicially depicts the ultramicroscopic, sub-Planck length landscape of the universe. To get a sense of scale, if we were to magnify an atom to the size of the known universe, the Plank lenth would barely expand to the height of an average tree.}

 

^{figure 5.1 is a picture of the computer image that the elevator and Greene were on in the clip.}

[timo]

Well, it´s nice that you take the time even quoting a passage of the book for me. But I´m afraid I won´t get it without seeing any kind of familiar formula. I´ll sleep a night about it and maybe ask a few people at work tomorrow.