# Particle Movement

1. Dec 28, 2009

### JerryMac

Does a elemental particle move through all points along a vector or does it move in "ticks" of a finite quanta?

Or in terms of waves and probability, if we measure the location of a particle at a certian time, will the particle be evenly distributed along all possible points of its vector?

Sorry if this is an invalid question. I am learning.

2. Dec 28, 2009

### DrChinese

Welcome to PhysicsForums!

You posted your question in Quantum Physics, so I assume you want the answer in quantum terms. Unfortunately, you cannot really make strong statements about a particle's movements in between position measurements at A and B. You have probably heard of the Heisenberg Uncertainty Principle, which applies to all fundamental particles. This limits our ability to make simultaneously precise statements about particle attributes. Some even question whether those attributes (observables) have simultaneous meaning or existence.

You may have heard of the path integral method, in which all possible paths are considered as contributing to the particle's trajectory. Due to the effects of constructive and destructive interference, the path tends to be a straight line. As far as anyone knows, the trajectory would not be considered a series of small "ticks".

Sorry to make a simple question into a complicated answer.

3. Dec 28, 2009

### JerryMac

Thank you for the response. I will study path integral method and Heisenberg Uncertainty Principle more. I really need to learn the math behind it!

4. Dec 29, 2009

### zonde

I like to think that elemental particle moves in "ticks". As I see it removes quite some weirdness from QM to view elementary particle as altering between non quantized interacting wave form and quantized non interacting particle form. But then I am just hobbyist so I am more free to think what I like.
And I would say that it might not go well with mainstream view because it requires local preferred frame.

5. Dec 29, 2009

### sokrates

Coherent movement and wave-function collapse are two different things, in fact these two are mutually exclusive.

Correct me if I am wrong but I had the impression that the "tick" you are describing is more related to the latter and it's a little different than an ordinary particle movement the OP is asking about.

So it's always like a non-quantized wave propagation (interacting or non-interacting).

6. Dec 30, 2009

### zonde

No, what I had on mind was not wave-function collapse. As I see wave-function collapse is related to ensemble but not a single particle and so it's irrelevant to question.
I was saying that particles "walk" in steps of their wavelength.

7. Dec 30, 2009

### qsa

in QM there is no notion of "particle" movement only wave funtion evolution and it moves smoothly. Then you can compute expectation values of the positions (using shrodinger equation) for the paticle in some potential and you will get the classical movement.

8. Dec 30, 2009

### Polyrhythmic

Well, one might take this question further and ask wether there is some kind of quantization for space, in which case such "tick-wise" movement might actually happen. I'm not sure if this is what the OP wanted to know though ;) This problem is solved neither in general relativity nor in quantum mechanics, hence it is subject of modern theories of quantum gravity.

9. Dec 30, 2009

### qsa

Quantum gravity theories have no bearing on particle movement question. theories linked to fundamental questions about QM do, like the Bohemian Mechanics and GRW theories. My own assessment shows that classical movement of particles is out of question.

http://www.qsa.netne.net

10. Dec 30, 2009

### Polyrhythmic

I think that it doesn't adress the question directly, but it's nevertheless an interesting line of thought. If spacetime was actually quantized, objects(including particles) would have to move according to this quantization, since spacetime is what they live in.

11. Dec 30, 2009

### qsa

QM( including all other conjectured theories) has aleady shown us weired nature of particle-wave daulity. It only gets worse in QFT which all QG theories are based on, you can hardly talk about particle movements. the theories only concern themselves with probabilties of outcomes of interactions and the strengths of the coupling of forces..etc. I agree that this is unfortunate situation, I myself trying to find if there is a way out.

12. Dec 30, 2009

### Polyrhythmic

In which sense can one not talk about motion of particles in QFT?

By the way, I tried to get the application you have on your website to run (the one in BASIC code), but I can't copy the code because it's an image, not a text.

13. Dec 30, 2009

### qsa

For one, the concept of field is used to represent streams of particles defined ofer a whole region of space-time, then the S-matrix is calculated from the in and out field to obtain the cross-section that is interpreted as probabilties of certain events occuring. you can google for s-matrix. The the Psi^2 probability density interpreted as position does not exist in QFT. I will get you the link that explains that later.

I have no problem in copy and paste (IE6). but here it is. you can play with it by changing the start position of the second particle (which acts as a potential barrier) st1 and its width d1 and see the interaction.

l = 500

t= 0

dim S(1000)

dim L(1000)

dim S1(1000)

dim L1(1000)

open "Draw" for graphics as #draw

for n=1 to 10
for j = 1 to 1000000

d1=4

st1=3

p= int(l * rnd(0))

li = int(l * rnd(0))

p1= st1+int(d1 * rnd(0))

li1 = int(d1 * rnd(0))

if p1+li1>p-li and p1+li1<p+li goto [q]

if p+li>p1-li1 and p+li<p1+li1 goto [q]

if (st1+d1-p1-li1)/d1 < rnd(0) then goto [qc]

if (-1*st1+p1-li1)/d1 < rnd(0) then goto [qc]

L1(p1)=L1(p1)+li1

S1(p1) = S1(p1) + 1

[qc]

if (l-p-li)/l < rnd(0) then goto [q]

if (p-li)/l < rnd(0) then goto [q]

L(p)=L(p)+li

S(p) = S(p) + 1

goto [q]

[q1]

goto [q]

[q2]

[q]

next j

for k = 1 to l

print k , S(k),S(k)^.5,L(k)/(S(k)+1)

tx=tx+S(k)

tn=tn+L(k)/(S(k)+1)

print sin((k*3.14)/l)*sin((k*3.14)/l)*y

next k

y=7.5*tx/k

print tx,tn/l

print #draw, "home ; down "

for r = 1 to l

print #draw,"goto "; r * 2 ; " "; S(r)*2

next r

print #draw, "up ; home ;color red ; down"

print #draw, "home ; down "

for r = 1 to l

print #draw,"goto "; r * 2 ; " "; S1(r)*1

next r

print #draw, "up ; home ;color red ; down"

for e = 1 to l

print #draw, "goto "; e* 2 ; " "; sin((e*3.14)/l)*sin((e*3.14)/l)*y

next e

print #draw, "up ; home ;color blue ; down"

for e = 1 to l

print #draw, "goto "; e* 2 ; " "; sin((e*3.14)/l)*y

print #draw, "flush"

next e
input a
next n

14. Dec 30, 2009

### Polyrhythmic

Thanks for the info, I'm quite new to QFT and willing to learn ;)

I'll try the code!

15. Dec 30, 2009

### qsa

here is the info I promised you.wiki QFT

"
Furthermore, the degrees of freedom in a quantum field are arranged in "repeated" sets. For example, the degrees of freedom in an electromagnetic field can be grouped according to the position r, with exactly two vectors for each r. Note that r is an ordinary number that "indexes" the observables; it is not to be confused with the position operator encountered in ordinary quantum mechanics, which is an observable. (Thus, ordinary quantum mechanics is sometimes referred to as "zero-dimensional quantum field theory", because it contains only a single set of observables.)

It is also important to note that there is nothing special about r because, as it turns out, there is generally more than one way of indexing the degrees of freedom in the field.""

In ordinary quantum mechanics, the time-dependent one-dimensional Schrödinger equation describing the time evolution of the quantum state of a single non-relativistic particle is

where m is the particle's mass, V is the applied potential, and denotes the quantum state (we are using bra-ket notation).

We wish to consider how this problem generalizes to N particles. There are two motivations for studying the many-particle problem. The first is a straightforward need in condensed matter physics, where typically the number of particles is on the order of Avogadro's number (6.0221415 x 1023). The second motivation for the many-particle problem arises from particle physics and the desire to incorporate the effects of special relativity. If one attempts to include the relativistic rest energy into the above equation (in quantum mechanics where position is an observable), the result is either the Klein-Gordon equation or the Dirac equation. However, these equations have many unsatisfactory qualities; for instance, they possess energy eigenvalues which extend to –∞, so that there seems to be no easy definition of a ground state. It turns out that such inconsistencies arise from relativistic wavefunctions having a probabilistic interpretation in position space, as probability conservation is not a relativistically covariant concept. In quantum field theory, unlike in quantum mechanics, position is not an observable, and thus, one does not need the concept of a position-space probability density. For quantum fields whose interaction can be treated perturbatively, this is equivalent to neglecting the possibility of dynamically creating or destroying particles, which is a crucial aspect of relativistic quantum theory. Einstein's famous mass-energy relation allows for the possibility that sufficiently massive particles can decay into several lighter particles, and sufficiently energetic particles can combine to form massive particles. For example, an electron and a positron can annihilate each other to create photons. This suggests that a consistent relativistic quantum theory should be able to describe many-particle dynamics.

I think my theory will be the real QFT but I would not bet any amount of money at this time. By the way I visited austria last summer, it is a nice country.