The discussion centers on the concept of wavelengths in relation to the Planck Length, specifically addressing whether a massive particle's wavelength can be less than the Planck Length when accelerated to high velocities. Participants confirm that while the de Broglie wavelength of macroscopic objects, such as a car, can indeed be smaller than the Planck Length, this does not imply that the Planck Length serves as a fundamental limit. The conversation also touches on the implications of quantum mechanics and the challenges of probing lengths at the Planck scale, emphasizing that classical physics remains applicable for objects whose wavelengths are smaller than their size.
PREREQUISITESPhysicists, students of quantum mechanics, and anyone interested in the intersection of classical and quantum physics, particularly in understanding the implications of the Planck Length and de Broglie wavelengths.
referframe said:It seems like if you accelerated a massive particle to a high enough velocity (momentum), you could get it's wavelength to be less than the Planck Length.
daisey said:I recently read that every object, including macro objects (cars, rocks, people) supposedly have wavelengths. I suppose that a car moving quickly might a wavelength smaller than the Plank Length. Sound reasonable?
Hyrox said:...I heard that it had been suggested that the Planck length was the smallest amount of space that it was possible to know anything about. Is this true?
daisey said:I believe I read somewhere that we could never generate enough power on Earth to probe lengths that small. And the Planck length is pretty small. I heard it described as follows...
If you could imagine a typical atom (which are pretty small themselves) expanded to the size of the known universe, the Planck length would be the size of a typical tree in that scenario. Now THAT is small!
It is not true.Hyrox said:I heard that it had been suggested that the Planck length was the smallest amount of space that it was possible to know anything about. Is this true?
Hyrox said:So, for a car weighing, say, one thousand kilograms, moving at 60 km/hr...
(6.62608 x 10^(-34) kg m^2 s^(-1))/(1000 kg x 16.667 m s^(-1)) =
3.97557 x 10^(-38) m
Since the Planck length is .616252(81)×10−35 m, you can see that the de Broglie wavelength of the car is much smaller, though I'm not sure what that means to us.
Bob_for_short said:It means it is smaller than the car size is, thus the car can be considered classically.
clem said:The Planck Length is not a limit on anything. It is just a dimensional number that is useful in some cases.
seniornegro said:We currently cannot measure or resolve anything with a λ shorter then h. We have to use probabilites and Quantum physics/mechanics for this. Its currently a limit which causes much confusion.
However, we see examples of this all around us.
Energy with a λ of h and shorter is what we call mass. Energy with wavelengths longer than h is what we call EMR / light / Radio waves.
From the equation E=hc/λ if λ=h then E=c. And energy of this level can no longer propagate at c (or radiate) and forms what we call sub atomic partilces.
An electron is a self contained wavelet energy function with a sub-h wavelength.
2.817939 × 10^-15 meters is the classic electron radius. 1.6 × 10^-35 meters is h. So ~1.75 x 10^20 cycles of a wave at λ=h could fit inside the electron.
The background medium we exist in resists these higher energy waves from propagating and limits the resulting energy particles (packets) from moving at c. Both c and h are a direct result of the characteristics of the background medium we exist in.
Remember that h is the quantum in quantum physics and quantum mechanics. Energy only exists in discreet increments of h. E=hv.
(IMO)
IttyBittyBit said:I've never heard of mass being energy with wavelength smaller than the Planck length. Please elaborate.
Yes and no; it makes no sense to talk about the velocity dependend energy; instead you must think about the invariant mass m² = E² - p²referframe said:It seems like if you accelerated a massive particle to a high enough velocity (momentum), you could get it's wavelength to be less than the Planck Length. Does that make sense?
It is a limit on the applicability of quantum field theory plus classical gravity!clem said:The Planck Length is not a limit on anything. It is just a dimensional number that is useful in some cases.