If a particle was at position X for zero time, was it there?

[sophiecentaur]

IMO, until one has a pretty thorough familiarity of the formalities of Calculus, one can’t start introducing Planck Time as an answer to questions like this one. There’s no proof that Planck units represent actual discrete steps so they just do not help.

 

[Dale]

however, the smallest measurement of time that has any meaning, and is equal to 10-43 seconds.

There is no indication yet that this is correct. It may eventually turn out to be correct, but we are quite far away from being able to justify this claim.

 

[Daniel Bolden]

There is no indication yet that this is correct. It may eventually turn out to be correct, but we are quite far away from being able to justify this claim.

i was just quoting wiki. i was implying that i believe, that the particle would at least exists in some form. though it may not be observable ,
or measurable, nor its state understood. but a zero interval = no change.
matrix A + zero matrix = matrix A. but there are a lot of great responses on this thread that are more sophisticated. i think it was a fun question.

 

[Dale]

i was just quoting wiki.

And I was just pointing out that the wiki comment is not based on any evidence. Wiki can be a good reference, but it also can get things wrong.

 

[Daniel Bolden]

if the particle was nudging its way up to x...almost there

A moving particle has been at position X for zero time. Was it ever at position X?
Can zero time be considered as never, as in "I was in Rome for zero amount of time."?
It seems like it would have been at position X if time passed in pieces the size of Plank time.

I've re-read the question. It seems to be saying the particle was moving in field Y for some time then passed onto field X for zero seconds. It never arrived into field X or position x. same as saying I drank zero cups of coffee this morning.

 

[Daniel Bolden]

And I was just pointing out that the wiki comment is not based on any evidence. Wiki can be a good reference, but it also can get things wrong.

my apologies. that was a bit of reaching. you caught that fast.

 

[ddjj77]

if the particle was nudging its way up to x...almost thereI've re-read the question. It seems to be saying the particle was moving in field Y for some time then passed onto field X for zero seconds. It never arrived into field X or position x. same as saying I drank zero cups of coffee this morning.

Why fields and not positions? Fields are infinite.
A moving particle has varying positions and has been at infinite positions for zero time at each position.

 

[Daniel Bolden]

Why fields and not positions? Fields are infinite.
A moving particle has varying positions and has been at infinite positions for zero time at each position.

you have been at zero positions if you have spent zero time anywhere. if a particle has passed through a gas cylinder for 2 thousandths of a second,
then it has spent 2 thousandths of a second passing through positions.

 

[ddjj77]

you have been at zero positions if you have spent zero time anywhere. if a particle has passed through a gas cylinder for 2 thousandths of a second,
then it has spent 2 thousandths of a second passing through positions.

That's my position too, but I want to find out if that's true. Has the particle been at any position?
Maybe the answer is in Heisenberg's uncertainty principle. If the particle is moving, then we can know its momentum, but not its position.

 

[Dale]

you have been at zero positions if you have spent zero time anywhere

That's my position too,

Your position is not self consistent then. In the opening post you specified that it had been at a position for zero time, which is inconsistent with it not being at that position.

 

[A.T.]

Maybe the answer is in Heisenberg's uncertainty principle...

Yes, but it's not really needed here. All you need is to realize that particles are not points in the mathematical sense.

 

[ddjj77]

Your position is not self consistent then. In the opening post you specified that it had been at a position for zero time, which is inconsistent with it not being at that position.

My opening was the question if being at a position for zero time amounts to having been at that position at all.

 

[Dale]

My opening was the question if being at a position for zero time amounts to having been at that position at all.

And clearly and obviously if it is at the location for 0 duration then it was at the location.

 

[ddjj77]

Yes, but it's not really needed here. All you need is to realize that particles are not points in the mathematical sense.

So, if a particle has a finite size (Planck diameter?), it would take a finite time for it to enter into and exit from position X, therefore it has been at position X?

 

[ddjj77]

And clearly and obviously if it is at the location for 0 duration then it was at the location.

Doesn't zero time mean never?

 

[Dale]

Doesn't zero time mean never?

No. Why would it?

 

[ddjj77]

No. Why would it?

Like zero speed means no motion.
Maybe there's no such thing as zero time. Maybe the shortest time is Planck time?
I'll accept your view for now.

 

[olgerm]

When the acceleration is zero it means the velocity isn't changing. Therefore the velocity would continue to be zero, meaning the ball would remain at its highest point. But it doesn't. As soon as it reaches its highest point it starts to fall.².

Consider particle with trajectory $x(t)=t^3$ at time t=0 it's acceleration and speed are 0, but it does not remain in point x=0.

 

[olgerm]

It is wrong to claim, that particle was not in some location $\vec{X}$ if it was there duration 0, because you can choose frame of reference where it is always moving(is never in rest). But answer to the question whether it was in that location must be same in all frames of reference.

 

[sysprog]

A moving particle has been at position X for zero time. Was it ever at position X?

A consistent description would depend on the size of the particle, on the size of position X, and on the speed of the particle.

If you imagine a photon that traverses a path from A to B, somewhere along which path is position X, then the answer to the question "was it ever at position X", is "yes", and the answer to the question "for how long a time", is "for however long it takes a photon to get from one side of position X to the other".

If position X is a mathematical point, with zero size, no particle of non-zero size could ever be entirely contained within its scope, so in that sense, that of the ordinary locational meaning of "at", the particle would not ever be "at" position X; however, the particle could be said to occupy position X for as long as any part of it were traversing position X.

If a photon, be it wave, field, or particle, has a positive finite size, and travels at speed of light, that size and speed will determine the size of a positive non-zero time interval over which the occupancy occurs.

It seems like it would have been at position X if time passed in pieces the size of Plank time.

The Plank time seems like a reasonable candidate for a minimum non-zero temporal duration.

If time is not continuous, but occurs in discrete instants, or chronons (Cornell U pdf article), then there is a minimum (non-zero) size of a (non-empty) time interval, and a particle that could reasonably be said to have ever arrived at a location would have to have arrived there at some, (at minimum single), chronon, but could presumably be posited to have remained at that location for zero chronons prior to the onset of its departure therefrom.

I think something like that is about as close as one can get to a consistent notion of a minimum size of a time interval over which, or during which, a moving particle could acquire a history of ever having been at position X.

Can zero time be considered as never, as in "I was in Rome for zero amount of time."?

In plain English it can.

 

[ddjj77]

If a photon, be it wave, field, or particle, has a positive finite size, and travels at speed of light, that size and speed will determine the size of a positive non-zero time interval over which the occupancy occurs.

Good point.
How about an electrical current in a one-atom thick conductor. As far as I can remember, it's not the same electron that went into one end of the wire that exits the other end. The entering electron causes the stationary electron in the first atom to jump to the next atom. In that sense all the electrons in a current have been at the position of every atom in the wire until each was kicked out of there.

 

[Dale]

Like zero speed means no motion.

Zero position means that you are located at the origin, not that you have no location. So that formulation is not always warranted.

In the specific case of your OP, it can be restated as given “Particle A was at position X for duration T”. Then clearly if that statement is given then the statement “Particle A was at position X” is true regardless of the value T, even T=0. This is a simple matter of basic logic and has nothing to do with physics per se.

Maybe the shortest time is Planck time?

As I explained above there is no evidence to support that claim.

 

[Daniel Bolden]

Your position is not self consistent then. In the opening post you specified that it had been at a position for zero time, which is inconsistent with it not being at that position.

I re-read the question...but my stance is constant : A + 0 = A. it depends on position of particle mentioned when clock was stopped.
no real particle is at any position for zero units of time, even if moving at relativistic speeds. even a photon is measured by its wavelength. therefore when moving across position x...from side A of photon to side B of the same photon takes some tiny duration...it is not zero units of time.

 

[Dale]

I re-read the question...but my stance is constant : A + 0 = A. it depends on position of particle mentioned when clock was stopped.

I have no idea what you are talking about. There is no mention in the OP about a clock being stopped. And while A+0=A is trivially true, it is also irrelevant.

 

[Dale]

The Plank time seems like a reasonable candidate for a minimum non-zero temporal duration.

There is no evidence to justify this.

 

[sysprog]

The Planck time seems like a reasonable candidate for a minimum non-zero temporal duration.

There is no evidence to justify this.

I don't think it's at all settled that there is such a thing as a minimum amount of time, or even a minimum spatial distance -- "seems like a reasonable candidate for" isn't a claim for the actual existence of "a minimum non-zero temporal duration".

The wikipedia "chronon" article (which is not very deep) says "The Planck time is a theoretical lower-bound on the length of time that could exist between two connected events, but it is not a quantization of time itself since there is no requirement that the time between two events be separated by a discrete number of Planck times." -- the "theoretical lower bound" characteristic is what I was thinking of when I said "seems like a reasonable candidate".

I think a minimum time interval size and a minimum spatial distance both imply a maximum frequency and minimum wavelength of light, which would seem to violate Lorenz invariance, and that apparent violation seems to me to be a significant problem not yet adequately resolved in such theories.

 

[Dale]

"seems like a reasonable candidate for" isn't a claim for the actual existence of "a minimum non-zero temporal duration".

Understood. I was only pointing out (again) that there is no actual evidence to justify it.

 

[Daniel Bolden]

I have no idea what you are talking about. There is no mention in the OP about a clock being stopped. And while A+0=A is trivially true, it is also irrelevant.

I apologize once again. A was supposed to be matrix A, describing anything you want about the whereabouts and state of the particle near position x.
Matrices are usually not dismissed as irrelevant describing particles in space and time.
OK, stopping the clock...i was referring to taking a slice of space with zero time elapsing. the batter hitting the ball(particle) as it crosses the plate(position x) for zero seconds(snap-shot) i.e. stopped the clock.
so... to have spent zero units of time somewhere? and still existed at that position? I'm not sold on either answer. like quantum particles. i'm
at more than 1 position at the same time. however
no particle physicist ever recorded a particle lasting for zero units of time at any position x.

 

[sysprog]

In the specific case of your OP, it can be restated as given “Particle A was at position X for duration T”. Then clearly if that statement is given then the statement “Particle A was at position X” is true regardless of the value T, even T=0. This is a simple matter of basic logic and has nothing to do with physics per se.

Not, "even T=0", but, except T=0. The word "was" means "existed in the past", and in your restatement , it is further predicated of particle A that its existence was "for duration T". If T=0 then "was for duration T" means "was not".

All durations of existence, for things that have ever existed, are positive non-zero durations. Even if the duration is possibly infinitesimal, it still must be greater than zero. Existing for zero time is the same as not existing.

You seem to think that as a matter of logic if you posit the existence of something, there is nothing you can further predicate of that something by which you can negate your positing of its existence.

However, duration of time of existence is a special predicate such that it cannot be assigned a value of zero without dis-preservation of the existence of that upon which it is predicated. Nothing takes place or exists or has ever existed other than in non-zero time.

If you disagree with that, I think you'll have a hard time showing that your position is one of logical necessity. That looks to me more like something that involves linguistic and ontic philosophy than like something that is purely a matter of logic. Defining for a first-order quantificational calculus a universe of discourse that expressly excludes any objects having a zero-value temporo-durational property would not render that system less sound or complete.

The following is intended to be in good humor:

/* pseudocode */

T=random(0 or 1) /* initialize duration counter to minimum of 0 or 1 */
If T>0 then /* if the event can happen, */
do while not arrived /* await it */  
   if arrived then /* if particle A has arrived at position X, */ 
   do while not departed until T=100 */ and has not immediately departed, */
      T=T+1 /* increment duration at position X (from 1 to 100) */
   end 
end
say "The duration of time for which particle A was at position X is" T
if T=100 then say "or longer"      
if T=0 then say "therefore particle A was never at position X"

 

[sysprog]

Understood. I was only pointing out (again) that there is no actual evidence to justify it.

Agreed.