Laymen artist needs equations

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1. Sep 7, 2015

renkma

I know this is a strange request; I certainly hope not unwelcomed here. I am not a physicist or a student of such, I'm just a humble tattoo artist in need of two equations - as I have a client that wants these equations designed into a piece:

1) the/an equation explaining the entanglement of particles

2) the/an equation explaining the outcome of the double slit experiment, when observed and the "wave" becomes particle.

I am attaching two equations I took screen shots of in a youtube video of a talk on these subjects, and although it was a professor of physics giving the talk, I don't want to take JUST his word for it that these equations are THE equations.

http://brainpanpublishing.com/entangled%20particles%20equasion.JPG [Broken]
http://brainpanpublishing.com/observed%20to%20particle%20equasion.JPG [Broken]

So would all of you very understanding and kind (and amazing) physicists out there please either agree that my attached equations are correct, or post the proper equations?

I very much appreciate everyone's help.

RE
New Graffiti

Last edited by a moderator: May 7, 2017
2. Sep 7, 2015

Geofleur

To make them into equations, you'll want there to be a "$|\Psi \rangle =$" on the left hand sides. So,

$| \Psi \rangle = \left( | \downarrow \uparrow \rangle + | \uparrow \downarrow \rangle \right ) / \sqrt{2}$

and

$| \Psi \rangle = \left( \Psi_U | D_U \rangle + \Psi_L |D_L \rangle \right) / \sqrt{2}$.

They look right to me.

Last edited: Sep 7, 2015
3. Sep 7, 2015

Staff: Mentor

Pretty much (although the second works better if the magnitudes of $\Psi_U$ and $\Psi_D$ are equal to one).

The first equation describes the state of a pair of spin-entangled particles. The second isn't about entanglement; it's the general expression for the polarization of a single photon.

4. Sep 7, 2015

renkma

Nugatory, I know the 2nd isn't entanglement.
2nd is apparently the equation that describes the wave / particle measurement problem - when observed during the double slit experiment ... is a particle rather than wave.
That is the 2nd equation I'm looking for.

And thanks Geofleur for your help.

5. Sep 7, 2015

ddd123

The double slit result is

$| \psi |^2 = | \psi_1 |^2 + | \psi_2|^2 + 2 | \psi_1 | | \psi_2 | \cos( \phi_1 - \phi_2 )$

6. Sep 7, 2015

Geofleur

ddd123, that equation is for calculating the probability from the amplitude but it might be better to keep the wave function expression so that this equation goes together better with the one for entanglement. Remember, it's a tattoo we're talking about here. It's supposed to look nice.

7. Sep 7, 2015

ddd123

That is the part where the particle detection law actually shows up, though. The wavefunction form is very implicit and can represent other things like polarization which has nothing to do with the double slit...

8. Sep 7, 2015

Geofleur

I see your point. Maybe it's better to stick with the amplitude squared after all...

9. Sep 7, 2015

ddd123

I think he should ask the client which one he wants.

10. Sep 7, 2015

cgk

First one (with the arrows) is much better (with the psi= on the left hand side, as Geofleur said in post #2). Everyone will understand the first one, it is effectively screaming "entanglement! That is me! looook at me, I'm entangled!!", and it does not need any further definitions. Second one does not do that to me..., in fact, without looking it up, I'm not sure what D_U and D_L are supposed to be... and quantum mechanics is my day job.

EDIT: you need to properly typeset the right angle brackets, though. They are supposed to look like in #2, not like "larger than" signs as in your original screenshots. That is important.

11. Sep 7, 2015

Geofleur

What if we write the double slit result like this:

$\langle \Psi | \Psi \rangle = \langle \Psi_R | \Psi_R \rangle + \langle \Psi_L | \Psi_L \rangle + 2Re \langle \Psi_R | \Psi_L \rangle$

Then at least R and L can stand for "right slit" and "left slit", the $\Psi$ would be capital in both equations, and the bra-ket notation would be used in both equations. Also the interference still shows up clearly in the "overlap" term.

Last edited: Sep 7, 2015
12. Sep 8, 2015

ddd123

I still prefer the subscripts 1, 2 instead of L, R but it's nicer now.

13. Sep 8, 2015

Heinera

I feel that we are still lacking some important physical information here, e.g. where on the body are these formulas supposed to be tattooed? Space might be an issue.

14. Sep 9, 2015

renkma

I love that so many got involved in this - thank you all so much!!

I do have to ask though, why is the "result of the double slit" equations all look so different from each other, and from the one I had initially found. I am really hoping for some agreement on this one.

The placement is inside the bicep for the double slit (represents to my client the "law of attraction" - unobserved, remains wave - observed, becomes a reality)
The placement for entanglement is center chest (with two roses - to my client, it represents her heart - her soulmate - I think it is a very romantic notion)
Space is not really an issue if the equations are reasonably short. I don't have room for a text book LOL

Because my client is a woman, I do definitely want the font to be beautiful for these tattoos. I've found some very decorative math and tech fonts to help me with design.

Thank you all so much.

Renee

Last edited: Sep 9, 2015
15. Sep 9, 2015

Demystifier

Just as with ordinary english language, with mathematical language one can say nearly the same thing in many different ways. And not all ways are equally "beautiful". In the double-slit case, the one in post #11 is probably the most beautiful so far.

16. Sep 11, 2015

ddd123

We all agree!

I strongly suggest you post the definitive version, since some fonts might make an equation look wrong.

17. Sep 11, 2015

dipole

Named functions should not be italicized. This is more correct.

$\langle \Psi | \Psi \rangle = \langle \Psi_R | \Psi_R \rangle + \langle \Psi_L | \Psi_L \rangle + 2\textrm{Re} \langle \Psi_R | \Psi_L \rangle$

18. Sep 11, 2015

Geofleur

Ah, right - the "Re" looks better that way!

19. Sep 12, 2015

bahamagreen

What a delightful thread; you know the ghost of Hilbert is watching this and grinning... :)

20. Sep 12, 2015

renkma

I will. Now, thanks to everyone's help here, I have my two equations and I will definitely post them with the fonts for everyone to look over for me ...

Geofleur - thanks so much. You've been such a huge help.

All of you - I'm just amazed at the response and assistance I received. I just love physicists!

And lastly, I will actually post the designs once they are finished ... AND the tattoos once they are done. :)