Wavelength Less Than Planck Length?

[LarryS]

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? As always, thanks in advance.

 

[Meir Achuz]

The Planck Length is not a limit on anything. It is just a dimensional number that is useful in some cases.

 

[Fredrik]

There's nothing weird about that, since spacetime is classical in both non-relativistic and special relativistic quantum mechanics. As for general relativistic QM, I think that's what loop quantum gravity is trying to sort out, but I don't know much about it.

 

[daisey]

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.

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]

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?

Definitely. The de Broglie of a macroscopic object is:

de Broglie wavelength = (h/momentum)

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. It's much too small to be measured.

To comment on what someone said earlier, 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]

...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?

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!

 

[Hyrox]

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!

Haha, yup. I've heard that exact same scale. I've also heard it scaled with a googol. The diameter of the observable universe is supposed to be just over a googol Planck lengths.

 

[Meir Achuz]

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?

It is not true.

 

[Bob_for_short]

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.

It means it is smaller than the car size is, thus the car can be considered classically.

 

[daisey]

It means it is smaller than the car size is, thus the car can be considered classically.

I think you are saying if the wavelength is smaller than the object it represents, "it can be considered classically". By "classically" do you mean not as a quantum object? I'm not familiar with your user of the term "classically" here.

 

[LarryS]

The Planck Length is not a limit on anything. It is just a dimensional number that is useful in some cases.

Some physicists believe that the Planck Length, or I should say Planck Area, limits the amount of information, in terms of physical structure, that can be squeezed into a given volume of space (black holes, Bekenstein Bound and all that stuff).

But, given a high-energy coherent beam of quanta whose wavelength is, say, 1000 times smaller than the Planck Length, one could conceivably store much more than 1 bit of information (amplitude modulation), in terms of spatial resolution, in one Planck Length.

 

[seniornegro]

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]

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)

I've never heard of mass being energy with wavelength smaller than the Planck length. Please elaborate.

 

[pallidin]

I've never heard of mass being energy with wavelength smaller than the Planck length. Please elaborate.

I second that. Do tell how you arrived at that.

 

[tom.stoer]

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?

Yes and no; it makes no sense to talk about the velocity dependend energy; instead you must think about the invariant mass m² = E² - p²

The Planck Length is not a limit on anything. It is just a dimensional number that is useful in some cases.

It is a limit on the applicability of quantum field theory plus classical gravity!

We know for sure that classical relativity cannot be quantized like any other field theory; there are a lot of hints that the usual quantization will break down. This breakdown is due to non-renormalizibility of (ordinary, metric) quantum gravity. Non-renormalizibility shows up at a certain scale; this is known in QED (where perturbation theory eventually breaks down due to the Landau-pole in the UV regime), QCD (where perturbation theory breaks down near the QCD scale in the IR). The only difference is that these two scales emerge only during quantization whereas the Planck-scale does already exist classically (gravity has an intrinsic scale as Newtons constant is not dimensionless, whereas the fine structure constant and strong coupling constant are pure numbers).

So it is by no means clear if it is M_Planck, 2*M_Planck or M_Planck/7; but it is for sure the order of magnitude of M_Planck, where a new theory called quantum gravity has to enter the stage.

 

[IttyBittyBit]

To be fair, out of all the crazy ideas that get posted on physicsforums.com, I'd have to say seniornegro's one is the most original I've seen so far. Everyone is focused on proving relativity wrong, or working around the Heisenberg principle, or whatever. But mass being 'high-wavelength energy'? Ingenious. I vote to make it Unconventional Idea of the Year.

Either that, or I haven't experienced too many wrong/crazy theories.