1+1 Dosen't Always Equal 2?! What?!

[Ralathon]

Not quite right - its not that the particles are destroyed. The idea here is that to measure the position more accurately, you need a higher frequency laser. The higher the frequency, the more energy the photon have so the bigger the "knock". You now have an accurate measurement of the position, but have no idea how fast the particle is moving after its knock.

That's the basic idea. I don't particularly like this description as it implies that the uncertainty principle is just due to "poor experiments" and that some bright spark could come up with a clever idea to get around it. If you believe in wavefunctions as "real" then the point is that well-defined position and momentum do not exist at the same time, not just that they can't be measured.

(P.S. I have a PhD in physics and K^2 is correct)

Yea a better way to explain it would be wave packets. Problem is that you need to explain a lot about how you can add waves of different frequencies to shape a pulse. Most people just get an information overload if you pile this on them.

[GreatWyrmGold]

Einstein didn't. Einstein, if I remember what you are referring to, discovered a formula which results in division by zero when particles with mass travel at lightspeed.

Name one particle which has been accelerated to lightspeed.

Your "layman's terms" explanation of Heisenberg's principle is wrong. It's impossible to *precisely* (meaning with absolute, 100% precision) measure both energy and momentum of a particle.

And that's all he requires for his initial argument to work.

Also, your statement that "it doesn't matter how you measure it" is perhaps the biggest lie in this thread - it does matter, and that's what things like "wave function collapse" and "Heisenberg's uncertainty" are all about. In fact, the biggest problem with quantum physics is that any measurement has a non-negligible effect on the system measured.

Exactly. No matter how we measure it, we're going to have those errors...and since we're never going to manage a perfect measurement, our ability to measure the velocity of a particle is even worse.

The point is, quantum mechanics won't let you perform miracles, nor "cheat" long established stuff like Newton's equations and thermodynamics.

...No one in this thread ever said that.

[andrewas]

Name one particle which has been accelerated to lightspeed.

Photons, according to KASAspace in the now locked thread where this started. He may have changed his tune since, but he was trying to argue that photons must have mass because they carry momentum.

In reality, of course, massless particles travel at lightspeed, massive ones travel below light speed, and Einstein's formula still gives you a division by zero if you plug lightspeed in as velocity without also having a mass of zero.

[Doozler]

Yea a better way to explain it would be wave packets. Problem is that you need to explain a lot about how you can add waves of different frequencies to shape a pulse. Most people just get an information overload if you pile this on them.

Yes, agreed of course.

...but when I'm king of the world, no one will be allowed to discuss the uncertainty principle without passing an exam in Fourier transforms

Edit: I sound a bit snide there! Seriously, I think this is one of those things that simply don't make sense until you have the maths. It never did to me!

Edited April 1, 2014 by Doozler

[KASASpace]

Photons, according to KASAspace in the now locked thread where this started. He may have changed his tune since, but he was trying to argue that photons must have mass because they carry momentum.

In reality, of course, massless particles travel at lightspeed, massive ones travel below light speed, and Einstein's formula still gives you a division by zero if you plug lightspeed in as velocity without also having a mass of zero.

Never said momentum, but according to Einstein, energy and mass correlated (which does not imply causation, I know).

Now since Photons, travelling at lightspeed (300,000 is actually rounded), have to have energy, so they must have mass.

However, Einstein probably did his second theory of Relativity which "found" a way through that..........

[PlonioFludrasco]

Ask Peter Higgs if (and why) a photon doesn't have mass.

(even if the right question is: why some particles has mass?)

[Ralathon]

Never said momentum, but according to Einstein, energy and mass correlated (which does not imply causation, I know).

Now since Photons, travelling at lightspeed (300,000 is actually rounded), have to have energy, so they must have mass.

However, Einstein probably did his second theory of Relativity which "found" a way through that..........

Actually you have it in reverse. Photons do have momentum but they don't have mass. If you derive the formula for momentum while taking the lorentz factor into account you get:

E² = (p*c)² + (m₀*c²)²

Where E is energy, p is momentum, c is the lightspeed and m₀ is the rest mass. If you take the velocity of the particle as 0 its momentum will be 0, so the first term falls away and you can simplify to the familiar E = m₀*c². In the opposite sense a particle with 0 mass still leaves the first term, showing that E = p*c. So a particle with 0 mass but some amount of energy will still have momentum.

[K^2]

Never said momentum, but according to Einstein, energy and mass correlated (which does not imply causation, I know).

Now since Photons, travelling at lightspeed (300,000 is actually rounded), have to have energy, so they must have mass.

There is a relativistic or inertial mass, which is related to energy by the famous E = m_relc². Photons have such mass.

There is an invariant or rest mass. This is what in modern physics we mean when we say just "mass". The correct equation that relates it to energy is E² = p²c² + (mc²)². Photons have no rest mass, and so we call them massless particles. For a photon, E = pc. All of the energy comes from momentum.

Gravitational mass is equivalent to inertial mass, as a direct corollary to the Equivalence Principle. So photons do have gravitational or heavy mass as well. They are both influenced by gravity and contribute to it.

[Doozler]

Einstein, if I remember what you are referring to, discovered a formula which results in division by zero when particles with mass travel at lightspeed.

...and "mass" in the above sentence means "rest mass, m_0"

So yes, photons have (relativistic) mass because they have energy, but they can travel at light speed because they have zero (rest) mass.

[Albert Einstien XXIII]

Arithmetic is fundamental  math theory- the basics. You can't understand algebra or other match theories without knowing arithmetic. Most people in this thread gave algebraic answers .  If "X" equal an apple, and  "Y" is an orange, how many apples do I have, how many oranges do I have or.... how many fruits do I have? The quantitative answer is two (fruits). The qualitative answer is 1 apple and 1 orange.  That's my two cents, for what it's worth.

I'm not a mathematician but I did sleep at a Holiday Inn Express. LOL  IYKYK.

 

[tater]

“You are a slow learner, Winston."
"How can I help it? How can I help but see what is in front of my eyes? Two and two are four."
"Sometimes, Winston. Sometimes they are five. Sometimes they are three. Sometimes they are all of them at once. You must try harder. It is not easy to become sane.”

[magnemoe]

Also depend on the numbering system 1+1=10 in binary as an example. 10+10=100 

[K^2]

46 minutes ago, magnemoe said:

Also depend on the numbering system 1+1=10 in binary as an example. 10+10=100 

These are different labels, though. I can replace label '2' with a label  and then 1 + 1 = , but that's still the same number, just written differently. 

It's much more exciting when 1 + 1 is equal to some other number.