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

[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.

 

[Dale]

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.

Correct. It is simply not possible for the statement “Particle A was at position X for duration T” to be true and for the statement “Particle A was at position X” to be false, for any A, T, and X. You can suppose that the first statement cannot be true for T=0, but given the first then the second statement is a direct and inevitable consequence.

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.

Sure, but under such a calculus the first statement could not be true, so such a calculus is irrelevant to the question at hand where the first statement is given as true.

 

[sysprog]

Correct. It is simply not possible for the statement “Particle A was at position X for duration T” to be true and for the statement “Particle A was at position X” to be false, for any A, T, and X.

It's possible for the statement “Particle A was at position X for duration T” to entail the proposition that "Particle A was at position X" only if duration T is non-zero. If duration T is zero, the statement “Particle A was at position X for duration T” is equivalent to the statement “Particle A was at position X for duration 0”, which is equivalent to “Particle A was for duration 0 at position X, which is equivalent to “Particle A was not at position X”.

 

[Dale]

I agree with that, but maintain that it's possible for the statement “Particle A was at position X for duration T” to be true only if duration T is non-zero.

That is your right to maintain, but it is not the topic of this thread where the statement was given to be true for T=0.

You should however note that the statement is a self consistent statement which is theoretically valid for classical point particles. To assert its falsity a priori requires a rejection of classical point particles. (I am ok with such a rejection, but not the arguments you have been using) Without rejecting classical point particles there is no valid objection to the statement, so since the statement is given as true it is reasonable to assume that classical point particles are the intended subject. My comments have been operating under that assumption.

 

[sysprog]

Correct. It is simply not possible for the statement “Particle A was at position X for duration T” to be true and for the statement “Particle A was at position X” to be false, for any A, T, and X. You can suppose that the first statement cannot be true for T=0, but given the first then the second statement is a direct and inevitable consequence.

If the first statement is true, and T=0, the first statement is itself the negation of the second statement.

Sure, but under such a calculus the first statement could not be true, so such a calculus is irrelevant to the question at hand where the first statement is given as true.

If the duration were non-zero the statement could be admissible, and true or false depending on whether the state of affairs was as predicated or not.

 

[sysprog]

It's not entirely uncommon to use zero time as negation:

Sergeant: Private, were you off base today without a pass?
Private: No, Sergeant, at no time today was I off base without a pass.
Sergeant: Were you at some time on some day other than today off base without a pass?
Private: Yes, Sergeant. but never since I first arrived at the base after being assigned here.
Sergeant: Carry on, Private.

That's of course not the same as "for a duration of zero time units", but the negating effect is the same.

 

[sysprog]

I agree with that, but maintain that it's possible for the statement “Particle A was at position X for duration T” to be true only if duration T is non-zero.

That is your right to maintain, but it is not the topic of this thread where the statement was given to be true for T=0.

You quoted (accurately) an earlier version of my post which I subsequently edited. To it I would append "if the truth of that statement is to entail the truth of the statement that "Particle A was at position X", if the truth of that statement is to entail the truth of the statement that "Particle A was at position X", so that the edited statement would read:

I agree with that, but maintain that it's possible for the statement “Particle A was at position X for duration T” to be true only if duration T is non-zero, if the truth of that statement is to entail the truth of the statement that "Particle A was at position X".​

You should however note that the statement is a self consistent statement which is theoretically valid for classical point particles. To assert its falsity a priori requires a rejection of classical point particles. (I am ok with such a rejection, but not the arguments you have been using) Without rejecting classical point particles there is no valid objection to the statement, so since the statement is given as true it is reasonable to assume that classical point particles are the intended subject. My comments have been operating under that assumption.

Let's please for a moment look at a proposed modification of the statement set to make the classic point particle paradigm more explicit:

The path of spatially dimensionless moving Particle A is posited to have intersected with 3 dimensional spatial point Position X, at time T' and for duration T, with duration T being zero and time T' being a specific instantaneous point in time on the timeline of Position X and on the timeline of Particle A. It is asserted that is not self-inconsistent to assert the existence of such a state of affairs, and further, that whether such a description is of a state of affairs that is factually possible in the real world is not decisively determined.​

This scenario being non-static, in that it references a moving particle, requires that the particle have a speed, that is, a distance which the particle traverses during a non-zero amount of time. If the amount of time is zero, the speed of the particle is infinite. This means that over the path the particle traverses at infinite speed, it intersects with all points simultaneously, so that it is being asserted to at time T' be at Position X, and also at time T' to be at other not Position X positions along its travel path. The notion of a point particle being at a specific spatial position at a specific point in time is inconsistent with the notion of it also being at some other specific spatial position, arbitrarily remote therefrom, at the same specific point in time.

It is not, ipso facto, logically inconsistent, unless it is further asserted that being at Position not X is logically equivalent to being not at Position X. It is equally possible to construct a consistent system of symbolization which would allow or disallow such translation. If we construct one which does not allow it, we cannot transform "being at Position X and being at Position not X" to "being at Position X and being not at Position X", because "Position X" and "Position not X" are atomic in this disallowing construction, so that the interior negation is not relocatable to the other side of the "at" in the expression "at Position not X", and so does not allow generation of the "at Position X and not at Position X" contradiction.

Whether the notion of infinite speed is self-consistent or not is a question that is system-dependent -- one could define the division by zero as equal to infinity, or declare it to be not defined, or take some other approach.

I see the original problem statement as systematically misusing language in a manner which produces unsatisfactory results in the attempts at answers. This is a problem with inquiry in general -- when we find that we've formulated a question clearly enough, we'll often have to re-examine foundations that we'd rather leave unperturbed. For how that quandary may be addressed, I see no deficiency to be ascribed in particular to either the person asking the question, or to anyone who tries to answer it.

 

[Herman Trivilino]

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.

You are of course correct. The context of my comment was a ball thrown upward, under the influence of gravity only. So the equation of the trajectory might be $x=19.6t-4.9t^2$.

 

[Dale]

If the first statement is true, and T=0, the first statement is itself the negation of the second statement.

No, it isn’t. The statement “Particle A was at location X for duration T” consists of the following three assertions: “there exists a particle A, a location X, and a duration T”, “A was at X”, and “the amount of time A spent at X was T”. So the second statement is indeed implied by the first.

a distance which the particle traverses during a non-zero amount of time. If the amount of time is zero, the speed of the particle is infinite.

It seems like your position is so untenable that you are being forced to ignore calculus to support it. You may want to rethink your position.

If a point particle has a finite velocity v(t) then the distance it traverses over a duration T is $$\int_{T’}^{T’+T}v(t)\;dt$$ which is 0 for T=0 regardless of v. To first order the time required to traverse a small distance $\Delta x$ is $\Delta t=\Delta x/v$ which clearly goes to 0 as $\Delta x$ goes to zero.

 

[hmmm27]

Remind me to never ask you guys to help my Uncle Jack off a horse : regardless of interpretation, both relative and equine would be high and dry. I kid , though I did spend enough time ruminating on dimensional interaction in 3+1 Newtonian space that not only do I not recall whatever TV episode was going on in the background, I'm not even sure what show it was.

 

[jbriggs444]

Remind me to never ask you guys to help my Uncle Jack off a horse : regardless of interpretation, both relative and equine would be high and dry.

If he was only up on the horse for an instant of zero duration then he'll be on the ground soon enough.

 

[hmmm27]

If he was only up on the horse for an instant of zero duration then he'll be on the ground soon enough.

That would be a point(s) contact for "Help my uncle get a leg over the horse".

 

[A.T.]

If the amount of time is zero, the speed of the particle is infinite.

Unless the distance traveled during that zero time is also zero. Then the speed is indeterminate, it can have any finite value. A position is just a point and has no size, so a point-like object travels zero distance, while being at that position.

 

[Vanadium 50]

I can't believe this is still going on.

You have a baseball traveling according to x = 2t + 1. At t = 3 you take a picture and sure enough, the photograph has a baseball at x = 7. Does anyone seriously want to argue that the baseball isn't "really" there? There's a picture and everything.

 

[hmmm27]

What I find interesting is that the OP's actual question - if he meant 2 0dim points - is non sequitur because - outside of a coordinate driven abstract, two 0dim points will never coincide : neither intersection nor duration. You need at least a total of 2 (spatial) dimensions between two objects to get an intersection, and at least 3 to get a duration of the intersection.