# Relative Velocity & De Broglie's Theory

1. ### DeepGround

15
Hello,

I would like to determine the Wavelength of many different macroscopic objects for a theoretical project and I am having trouble understanding how to use the equation correctly due to relative velocities.

When computing Wavelength = h/ Velocity * Mass I see example of calculating the wavelength of a baseball that is moving at 40 meters per second and weighs .14 kg.

So I see that I need to use Meters per Second for velocity and KiloGrams or 1000x Grams for Mass. The trouble is that Velocity is relative, so this only gives you a wavelength of a baseball relative to the earth.

I do not understand what the earth has to do with the wavelength of the baseball, are all wavelengths only relative? Is there no wavelength for the object itself? This means that the baseball has a huge amount of wavelengths depending on how you look at it.

Also Plank's constant can be written in many different ways, and be different numbers. How would I know what number to use when I am talking of velocity in meters per second and mass in 1000x grams.

2. ### Tom Mattson

5,538
Staff Emeritus
The Earth has nothing to do with the wavelength of the baseball. It's the frame of the Earth that matters.

Yes.

Well, in relativity one refers to quantities such as the length of an object or the lifetime of a particle in the rest frame as the "proper length" and "proper time", respectively. We can't do that with deBroglie wavelengths however, because $\lambda=h/p$. In the rest frame of the baseball, $p=0$, and $\lambda$ is undefined. So the answer to your question would be "no".

Since m/s and kg are MKS units for velocity and mass, respectively, it would only stand to reason that you use Planck's constant in MKS as well: $h=6.63\times10^{-34}Js$

3. ### DeepGround

15
Thank you Tom for the quick reply!

I will start tryng to bend my mind around relative wavelengths, and I looked up an MKS table, that is very helpful, thanks again!

4. ### peter0302

869
Correct me if I'm wrong, but the de broglie wavelength would have to be relative to the observer, just as all lengths are, otherwise different moving observers would see different interference patterns in a Young double slit experiment.

5. ### Tom Mattson

5,538
Staff Emeritus
Funny you should mention that, because I posted a thread on this very question some time ago.

The deBroglie wavelength in fact doesn't transform as a length. It transforms as an inverse length. That's because of the presence of the momentum in the denominator of the deBroglie relation. Momentum transforms just like length does.

6. ### DeepGround

15
Can you explain what you mean by the difference between a length and an inverse length.

Despite the fact that the wavelength is inversly proportional to the velocity I still think that if you get a different wavelength you get a different length of the wave period.

AND if you change the velocity or anything in the denominator you get a different wavelength.

Soooo wouldnt that mean that the length of the period of the wave transforms based on observers?

I tried reading the other thread you posted but it started to get to complicated for me :)

7. ### Tom Mattson

5,538
Staff Emeritus
Simply put: If x is a length, then 1/x is an inverse length.

Sure, the wavelength is different in different frames. But it's not enough to say that it's different. The real question is "how different?" How do you calculate the difference? As I said, it doesn't transform as a length, as one might naively expect. It transforms as an inverse length.