proton

What does the merged part mean?

 

I had forgotten to mention the HUP so when I came back and added that comment it merged the two posts together. I think I was too late to edit it and that's why I had to quote myself.

I would love to understand and am very interested in what you just said.

I'm both encouraged and surprised by your interest. It's heart warming to see such a keen interest in the physics as your displaying here. I'm also surprised because I would have thought that most people wouldn't concern themselve with this. I'm pleasantly surprised.

Is this, in effect, a mathematical statement of the uncertainty created by trying to measure a particle?

The idea that uncertainty is created by trying to measure a particle is an urban myth. It is more accurate to say that uncertainty is intrinsically inherent in the system rather than related to measurement. E.g. ideally, no matter how you choose to measure the properties of the system, the uncertainty remains unaffected and is dependant only on the state of the system. This means that once [math]\Psi[/math] is determined [math]\Delta x[/math] is determined. Or to be more precise, once you tell me what [math]\Psi[/math] is I can tell you the value of [math]\Delta x[/math] and I don't need to know anything about how you intend on measuring the postion.

Where attenuating the frequency of the magnetic field for momentum decreases the accuracy of the measurement taken by the same device for position and vice versa; with respect to plancks constant of coarse......

The A above refers to a classical uniform magnetic field. There is no frequency associated with it. The associated quantity B_z represents z-component of the magnetic field determined by A.

Thanks for your input Proton! It's those little bits I don't know to look for that often hold me back from seeing the big picture.

Your very welcome. I admire that attitude. Shows courage in the face of the scary quantum world!

 

One of the rewards of posting here is the satisfaction I get from seeing people enjoy physics and knowing I was able to help. It kind of makes up for those arguements with the resident thought police.

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I forgot to mention that the HUP relation for position and momentum are unaltered in this case.

Ok then, minus the forces.

It should be noted here that at present, energy can't be properly defined when gravity is present. It should also be noted that there is positive energy from things like rest energy and negative energy from the negative gravitational potential energy. It's possible that the total energy could be zero.

 

Paul Davies expresses this as follows. From God & the New Physics, page 31 (Don't let the title of this book fool you. The author is what I'd refer to as an authority in the field of astrophysics. His homepage is http://cosmos.asu.edu/)

There is still a more remarkable possibility, which is the creation of matter from a state of zero energy. This possibility arises because energy can be both positive and negative. The energy of motion or the energy of mass is always positive, but the energy of attraction, such as that due to certain types of gravitational fields or electromagnetic field, is negative. Circumstances can arise in which the positive energy that goes to make up mass of the newly-created particles of matter is exactly offset by the negative energy of gravity and electromagnetism.

...

Some have suggested that there is a deep cosmic principle at work which requires the universe to have exactly zero energy.

...

Matters are further complicated by the fact that energy is not even properly defined when gravity is present.

dude! purple text = bad.

 

pT=b

 

also

 

(bT) + (pT) = vb

Thanks GutZ. I'm quite aware of that. I know that it was a standard message. I was expressing my displeasure at the existance of this thread. It was created on two premises (1) that I have a crusade and (2) that I want to change how people talk. Both premises are wrong. I really only made (or wanted to make) two points in this thread and have succesfully argued them (1) I'd rather leave than have the way I choose to explain physics censored and (2) I never have and never will be anything but 100% clear as to what any term I use means. The use of rel-mass was something I posted in another thread and I don't see that it's useful to repeat myself. I also choose not to argue about the usefulness of the concept since its clearly a matter of taste and arguing about it is like arguing about whether red or blue is the nicer color. How this affects how I use the term momentum in the future is now making me wonder. I never gave that much thought until I came up with that example.

 

I resent your claim that I posted misinformation.

I appolgize if you were offended. That wasn't my intention. The term misinformation is defined as inaccurate information that is spread unintentionally. Perhaps you prefer another phrasing, e.g. what klaynos posted is emperically incorrect etc. This is a well known fact and is expressed in the journal articles written by the people who are trying to ban the concept. In fact one of the reasons they keep writing these articles is because physicists still use it. Not only physicists by chemists and astronomers etc use it too.

 

This is getting sillier by the second.

 

Fact - Whatever is posted in this thread after this post I hereby promise you will go unread. If I read anymore false assertions about what I have or will post I will not be happy and might feel inclinded to correct them - again!

 

Proton - out.

Yeah it's a bit much for me lol.

 

btw lol (laugh out loud) I say it all the time and forget not everyone is down with internet lingo.

I read an article on this. If there is no magnetic field then p = mv and [math]\Delta p_x \Delta p_y = 0[/math] which means that [math]\Delta v_x \Delta v_y = 0[/math]. When there is a uniform magnetic field present then this becomes

 

[math]\Delta v_x \Delta v_y > e\hbar/2m^2c |<B_z>|[/math]

 

This would not be apparent if one didn't know how p is actually defined.

Proton:

 

For me not so much because I don't know when that would be relevant.

 

when does the cannonical momentum become crucial to add?

What do you mean "crucial to add"? If you mean when it is important to know what quantity appears in the equations then, for example, when its a charged particle moving in a magnetic field. In that case the momentum the HUP refers to is cannonical momentum and depend on the magnetic field. As I said, this is an advanced topic. But I wished I knew about if when I first learned quantum and not when I studied it as an upper classman

.. within 24 hours it will no longer be active and as such, slightly more useful.

 

It should have been locked a long time ago. In fact it never should have started. Especially not in this forum since the subject matter in the first post is neither pseudoscience or speculation. One can hardly claim that subject matter in the American Journal of Physics can fit into those categories.

 

It was hardly off-topic either since I was correcting the misinformation posted by Klaynos.

The thread starter has failed or is failing to support their position, ..

Since Martin started this thread, what position are you claiming that he failed to support?

 

I do agree, however, that Martin failed to prove that I want to change the way people use terminology.

If there's no discussion, stop insisting there is one.

Huh? I said I won't be dragged into a debate and most of the posts here are designed to do so. I never claimed anything else.

Regardless, I don't quite see how you would be in any position to give any moderator "advice" on how to run threads.

If you don't care what people want then ignore the suggestion. Simple. If the forum prohibits posters from making suggestions then it should be in the forum rules. When I see it there I will stop making suggestions.

I do recommend you make your point already ...

I made my point before this thread was started.

and stop insisting you're the only person in the world who knows physics the way physics is supposed to be.

What a silly thing to say. I never made such a claim. I can't fathom how someone could jump to such an obviously false conclusion. Only an extremely arrogant person would think such a thing. In fact I've only argued that I will explain physics in a way that I think works best. Please pay closer attention to what you're reading.

 

I have to admit that most of my resposes were to correct false accusations made against me. I find it hard not to correct someone who says something about what I've posted/said or will post/say that is not true.

I'd kiss you guys...good thing this is a forum!

 

*dances with glee*

 

I still need to do some research and take a few math classes, but I am not hopeless it understand it seems.

 

joy.

I'm going to try an experiment here. There is a debate on terminology in another thread and I want to try something here to see what happens.

 

You know that the uncertainty principle relates uncertainty in momentum to the uncertaintly in position, right? What you don't learn until advanced courses on quantum mechanics the momentum this refers to is actually what is called "cannonical momentum" (aka conjugate momentum). Its different than the momentum p = mv (small p) that you learn about in basic physics. Suppose a charged particle is moving in a magnetic field. The cannonical momentum p has the value

 

(B-45) p = mv + qA

 

where A is known as the magnetic vector potential. A graduate text by Cohen Tannoudji explains this (page 225) as follows

Care must be taken not to confuse p (the momentum of a particle, also called conjugate momentum of r) with mv (the mechanical momentum of the particle): the difference between these two quantities appears clearly in (B-45). ...However it is the conjugate momentum p and not the mechanical momentum mv which becomes in quantum mechanics the operator P which satisfies the canonical commutation relations.

Since canonical momentum is a rather advanced topic and probably not known to most visitors here I'm curious as to whether such a fact is of interest to anyone, i.e. would you want to know that p is a function of the magnetic field through the quantity A? Thanks for your input.

 

Mod note: moved to its own thread

Would it be accurate to say the entire universe -- minus the known forces -- is all energy?

No. That would be like saying "This apple is energy." The apple is not energy. It merely has energy.

 

Why the comment about minus the known forces? Forces give rise to potential energy.

Alrighty then, there's no point in a discussion, is there?

 

~moo

I kept saying that above many times. You'd be wise to lock this thread otherwise everyone will keep trying to draw me into a deabate that I had stated I will not participate in.

..but that will not change the fact that if you don't start using conventional, *CLEAR* definitions,.

This is another example of a poor arguement. You'r claim that I don't use clear definitions is bogus. You would never be able to find a post where the definition of any term I used was not 100% clear. I can't help it if this simple fact is not getting across to you.

 

And don't give me this nonsense about experts since I personally know plenty of experts in various fields of physics who publish just as much, if not more, than the people here - whom I have no idea who they are by the way. And those people would never present such arguements in their lives. Don't confuse the people who choose to post in discussion forums as being representative of the fields.

 

You're said you're an undergraduate. I've been a physicist for over 20 years so please don't give me this nonsense you're now giving me about so called authorities.

 

And I find your attitude quite poor. Chill out please. Moderators should not be so irritating.

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I know you'd strongly argue your point. The problem being, you wouldn't be arguing about the same point that others are arguing about. That's why there's no value in it.

You posted an arguement based on the notion of "common terminology." I responded to that post by asking you to define the term momentum so I could make my terminology. So your claim that I'm not arguing the same point others are is quite incorrect.

 

You are referring to other arguments made by people here. I find them to be poor arguments and I know that people are pretty closed minded in this subject so I choose not to participate.

If someone uses "mass" to mean rest mass, and someone else uses it to mean relativistic mass, it will cause confusion, since they are not interchangeable.

This is a perfect example of what I meant by a poor arguement. You keep assuming that I intended to use or have in the past used the term "mass" to mean something besides "rest mass" even though I explained in great details this has not happend and is not going to happen. I explained this several times. There is no example where people are not 100% clear on what I mean. If I choose to say "Below by mass I will mean relativistic mass" it is only to make the writing easier for me since its easier to write mass than relativistic mass. It is just for the sake of ease of typing, nothing more. And when that is said its not possible to make a mistake on what the term means. This is the same idea of saying in the quantum section "Below by momentum I will mean canonical momentum".

Do waves really go on forever?

Depends on the precise definition of that term. E.g. a sine wave is infinite in extent. In practice it's finite. For example; for a particle in a box the wave is non-zero inside the box and zero outside. If a particle is represented by a Gausian wave then it's large near its peak and drops off as one gets further from the peak, but mathematical never equals zero but is close enough to zero for any practical purpose.

So you need a wave to be in a specific eigenstate to get a precise value?

No. You need the state to be an eigenstate to be sure of the value you get. Any measurement yields a value whose precision depends only one the experimental set up and instrumentation used. The precision is independant on the nature of the wave.

A wave a can either be localized or plain wave, and It just so happens that one state gives you precise position and the other momentum, and because you can't measure something that is in both states at once we are limited to know either one or the other precisely?

Yes.

Why would it be a sum of alot of plain waves?

An arbitrary state is not a simple one. But any arbitrary state can be represented as a superposition of eigenstates (e.g. plain waves). Sound is like that. Any sound can be reduced to a superposition of sines and cosines.

Okay, proton, you seem to have missed swansont's point.

I understand his point quite well, thank you. I hope we're not going to get into a debate about whether I undertand his point now, are we??

Regardless, I'll answer your question:

 

The physical definition of momentum is p=mv

 

Mind you, relativistic momentum is slightly different.

 

Photon momentum, for that matter, is entirely different:

(source: http://frank.mtsu.edu/~phys2020/Lectures/Part_2__L6-L11/L8/Relativistic_Momentum/body_relativistic_momentum.html )

 

Thanks for answering. Now I can make the point I've wanted to for days now!! Just to make sure that there is no confusion about what my point will be let me recall for you why I asked this question. Recall what swansont wrote

If what I mean by mass is different from what you mean by mass (or whatever term you wish to choose)' date=' then the discussion grinds to a halt right there. Common terminology is like the "handshaking" the fax machine (or any other communication protocol) does at the beginning of the transmission. Without it you are lost. You are Humpty Dumpty, saying, "When I use a term, it means whatever I choose it to mean — "nothing more, and nothing less," and then it's impossible to discern what was actually said, because none of the words are meaningful to anyone else.

[/quote']

If you have a lot of experience reading physics literature then you might know that this rarely if ever happens, even when the same exact term is used. The context almost always tells you the meaning of a term. And if not once one states what one means there can be no confusion. In other cases I've explained things in the following way. When someone once asked me something like whether the gravitational field of a body is a function of the body's speed. I responded with something like "The mass of the body (whereby mass I will mean relativistic mass) varies with speed and this ends up meaning that the gravitational field also depends on speed, the field of which is rather complex so one has to be careful." I qualified what I said because its a pain to keep writing "relativistic" before mass in each and every instance. So I made it clear that this was what I was doing. Thus the context determines the meaning.

 

Now the particular branch of phyysics can also determine the meaning of a term. In analytical mechanics the term "momentum" means canonical momentum and that can end up being angular momentum if the conjugate variable is an angle. In Newtonian vector mechanics momentum is defined as p = mv, i.e. linear mechanical momentum. Same in relativity if the m is relativistic mass (which was what motivated Richard C. Tolman to define it as such). However if you were to pick up a quantum mechanics text then this would not be true. In the context of quantum mechanics the term "momentum" means "canonical momentum". In applications like a charged particle moving in a magnetic field the linear mechanical momentum is different than the canonical momentum. This is an important point that I'm sure most people are unaware of. However if you were to pick up a relativity text then the term "momentum" might be 4-momentum. MTW does this but the authors are very clear on what they mean.

 

So there is

 

(1) Linear mechanical momentum

(2) Canonical momentum

(3) 4-momentum

 

Telling me not to refer to relativsitic mass is like saying never use the term "canonical momentum" or "4-momentum".

There's no value in answering it.

That is quite incorrect. If you'd answer the question then you'd see that the purpose of it has everything to do with this thread and the points you attempted to make. It's such a trivial and easy question. I suspect that you know that I'd strongly argue my point if you responded and that is why you refuse to do so. I challenge you to prove me wrong by posting the definition of momentum. After all it was you who claimed that we all have to mean the same thing by each term or confusion arises, did you not? So post what "everyone" means when they write the term "momentum" please.

 

Then again if you refuse to answer it also demonstrates my point quite well too.

You seem to be arguing a different point than everyone else in this thread.

Wrong. The people who posted in this thread want to debate the usefulness of rel-mass. I never had a desire to debate the concept since it's a fact that any such debates is ultimately a waste of time. You can't argue about what is useful to one person because everyone thinks differently. I've only responded to correct misinformation that has been posted in this thread, e.g. what I supposedly wanted people do do etc.

That would work in principle, if the line of charge was infinite. If not, at some point the charge would stop.

It really makes no difference the shape or extent of the charge distribution. Charge at rest in one frame means that there is current in another frame moving relative to that frame.

Just because you've stopped looking for the wave behavior doesn't mean it's not there.

Who said it wasn't there? Not I. I said that wave nature and quantum nature are not the same thing. I also said that when a quantity is measured in discreetly quantized systems the result is precisely determined. What part of that are you suggesting is wrong?

We weren't discussing the complications that arise when you treat this relativistically.

Obviously. But that doesn't change the fact. The reason it transforms differently is that energy in motion is defined differently than heat. Ignoring context leads to errors in application. Heat is defined as the flow of energy from one object to another caused by a difference in temperature. The cause of light from a laser is not caused by a difference in temperature so one can't call the radiant energy from a laser "heat". Heat is also the quantity Q in the relation

 

[math]\Delta U = Q + W[/math]

 

That relation defines Q and is why it transforms differently than energy. You seem to think that any energy which flows is called heat, for what reason I can't see. Since this is going nowhere so I have nothing left to say.

You didn't answer my question. Can you give me a single property that is not (quantum) wave like?

You used quantum to be synonymous with wave so your question has no meaning. I already gave you an example, i.e. spin. Spin is not wavelike. Anything which has a discrete spectrum is like that. When a measurment is made on a discrete system for which there is a uncertainty in the quantity being measured one can theoretically obtain precise values. Hence the difference between uncertainty in a state and the absolute precision of measured value.

Irrespective of terminology, I hope you agree that the statement "you have some misconceptions about the wave-particle duality" has no worth in debate.

Debate!? Nobody said anything about debate. I was merely saying that your responses represented what I consider to be misconceptions. If it will help you move on then I rephrase my comment as "That remark represents a misconception."

 

Back to physics - Theoretically the eigenkets of position are defined as

 

X|x> = x|x>

 

where X is the position operator and x is an eigenvalue of position. An arbitrary state can be expanded in terms of these eigenstates as

 

[math]|\alpha> = \int dx|x><x|\alpha>[/math]

 

A highly idealized experiment might be to place a very tiny detector that clicks when a particle is at x and nowhere else. After it clicks we say that the state is represented by |x>. I.e. we say that [math]|\alpha>[/math] jumps to |x>. However in practice one normally can only locate the particle to a narrow interval about x. So the state goes from [math]|\alpha>[/math] to [math]\int dx|x><x|\alpha>[/math] where this is integrated over the width of the detector. If the particle is located within this range the detector clicks. This is, by definition, a particle property. Your assertion about variance means that the width is non-zero. But your comments about it suggest that there is no particle phenomena here which is misleading. The "click" means that the particle is localized in the sense defined above. That's what the term particle means and what was meant by the Dirac function being represented in practice by a step function. Interpretation is a key point here. Point particle means that there is no theoretical limit to the smallness of the detector.

 

The reader can read more about this in Sakurai in the section Position Eigenkets and Position Measurements.

 

No it isn't. Please provide evidence of an experiment which has provided a position measurement with infinite precision.

I was speaking in general terms, not about position. If you read my comment more carefully you'd have noticed that since I wrote This happens when there is a discrete spectrum of eigenvalues. Obviosly position has a continous set of eigenvalues.

Why not?

I explained above.

Please provide evidence of an experiment which has provided a position measurement with infinite precision. I would be very interested to hear about it.

Please reread what I wrote, i.e. determined with infinite precision. Consider a measurement of the spin of an electron. There can only be two possible values which are theoretically determined with no uncertainty.

Please debate the science, not the credentials of the debater.

Credentials???? Just because it's my opinion that you have a misconception, as reflected in your response, it has absolutely nothing to do with credentials.

Yes, it includes radiant energy.

In relativity heat transforms differently than energy. So one cannot merely make the assertion the blind assertion that radition is heat.

Hence why Severian says "Everything is a (quantum) wave, period." The quantum in brackets is important for this discussion.

That doesn't appear to be what Severian meant since he wrote

So even right after a position measurement, particles are still waves.

Everything in the universe is really a wave, and the HUP is really just coming out of the properties of waves.

I wouldn’t phrase it like that myself. Particles cannot be said to “really” be a wave. That contradicts the wave-particle duality. The whole idea is that they have wave properties and particle properties. Do you recall how Feynman explained this? From his Lectures, V-III page 1-1

Newton thought that light was made up of particles, but then it was discovered that it behaves like a wave. Later, however, (in the beginning of the twentieth century), it was found that light indeed sometimes behaved like a particle. Historically, the electron, for example, was thought to behave like a particle, and then it was found that in many respects it behaved like a wave. So it behaves like neither. Now we have given up. We say: “It is neither.”

For example, a "particle" is something which we think of as being very localised in position. It is in one place. But of course, our measurement of that position is never infinitely perfect, so it is really just a wave which is very very peaked it the point we think the particle is. This is the wave/particle duality thing.

Actually our measurement of its position can be made with arbitrary precision regardless of what the uncertainty in position is.

 

To Gutz: Wave-particle duality is really just something we use to frighten children and undergraduates. Everything is a (quantum) wave, period.

Where did you get such an idea?? Nothing could be further from the truth.

We teach undergrads that the wavefunction has collapsed into a position eigenstate, but this isn't quite correct, since it has collapsed into a superposition of position eigenstates, localized around a point, with an variance given by the error of our measurement. So even right after a position measurement, particles are still waves.

Not true.

Your first comment is correct. When a measurement is made the state falls into one if its eigenstates, not a superposition of them. I.e. when the position is measured the state is |x>. Since no measurement has infinite precision there delta function might actually be approximated by an extremely narrow step function. But that doesn’t mean that it’s a wave and not a particle. And as I stated above, the imprecision of a measurement has nothing to do with uncertainty. It's quite possible for a system to have a finite uncertainty and for a measurement to be made in which the result is determined with infinite precision. This happens when there is a discrete spectrum of eigenvalues.

 

Nothing personal, but I’m afraid that you have some misconceptions about the wave-particle duality.

swansont - the only reason I'm checking this thread now is to wait for your response to my question regarding the definition of momentum. Please either respond to it or state in no uncertain terms that you won't be responding to it. I'm not sure if you keep missing it of choose not to answer from some very odd reason. I find it quite odd that you don't mind asking me all sorts of questions but the one question that I ask goes totally ignored. Why do you suppose that is?