Impossibillity of measurement at time t

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Impossibillity of measurement at time t

#1  Postby heisenbinker » Sep 02, 2011 7:42 am

If we carry out the thought experiment for the uncertainty principle : i.e. the photon hitting the electron under a microscope.

For this experiment to be of quantum nature the observation is compulsory and the photon has to hit the electron.

Now, say you want to observe the position at time 't'.

And say for convenience sake you can setup the experiment and perform it instantly.
Two separate points i would like to make are

1) For the photon to hit the electron it has to travel a distance 'd' and collide with it. The time taken would be d/c. where c is the speed of light. So the observation is made at t+ d/c. The time for the photon to be observed by the observer can be neglected from the fact that the observer is watching on the plane adjacent to the collision, an infinitely small distance away.

2) There is a probability that your photon will not hit the electron instantly because the photon has a linear (?) trajectory and miss the electron since we don't know where it is. This probability should depend on all possible points in space that can be occupied by the electron and how fast the photon can traverse through this space (by means of rebounds or whatever) which is certainly finite, hence at time t you will never ever determine the position x certainly.

Am i right in thinking this?
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Re: Impossibillity of measurement at time t

#2  Postby cavarka9 » Sep 02, 2011 8:44 am

heisenbinker wrote:If we carry out the thought experiment for the uncertainty principle : i.e. the photon hitting the electron under a microscope.

For this experiment to be of quantum nature the observation is compulsory and the photon has to hit the electron.

Now, say you want to observe the position at time 't'.

And say for convenience sake you can setup the experiment and perform it instantly.
Two separate points i would like to make are

1) For the photon to hit the electron it has to travel a distance 'd' and collide with it. The time taken would be d/c. where c is the speed of light. So the observation is made at t+ d/c. The time for the photon to be observed by the observer can be neglected from the fact that the observer is watching on the plane adjacent to the collision, an infinitely small distance away.

2) There is a probability that your photon will not hit the electron instantly because the photon has a linear (?) trajectory and miss the electron since we don't know where it is. This probability should depend on all possible points in space that can be occupied by the electron and how fast the photon can traverse through this space (by means of rebounds or whatever) which is certainly finite, hence at time t you will never ever determine the position x certainly.

Am i right in thinking this?


welcome :cheers: except you havent yet said what exactly is your equipment for measuring time?. The problem with time is that there is no uniquely independent way of even measuring it, it can be done only in relation with something else.

1). true, there is gap between measurement and observation, but it again depends on your experimental setup, how do you make an observation.
2). While there is the issue of probability without doubt, you could consider averaging over some n trials.

thirdly, the uncertainty principle has relations between energy and time, position and momentum, angular position and angular momentum. So theoretically one could get position and time accurately, it now depends on your experiment.
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Re: Impossibillity of measurement at time t

#3  Postby twistor59 » Sep 02, 2011 9:59 am

heisenbinker wrote:If we carry out the thought experiment for the uncertainty principle : i.e. the photon hitting the electron under a microscope.

For this experiment to be of quantum nature the observation is compulsory and the photon has to hit the electron.

Now, say you want to observe the position at time 't'.




If you're talking about a Heisenberg Microscope - type experiment, do you really need to worry about the time of the position observation ? Isn't it the case that we're just concerned with the uncertainty in the position ?
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Re: Impossibillity of measurement at time t

#4  Postby heisenbinker » Sep 02, 2011 10:08 am


cavarka9
welcome :cheers: except you havent yet said what exactly is your equipment for measuring time?. The problem with time is that there is no uniquely independent way of even measuring it, it can be done only in relation with something else.

1). true, there is gap between measurement and observation, but it again depends on your experimental setup, how do you make an observation.
2). While there is the issue of probability without doubt, you could consider averaging over some n trials.

thirdly, the uncertainty principle has relations between energy and time, position and momentum, angular position and angular momentum. So theoretically one could get position and time accurately, it now depends on your experiment.




The experiment is not mine. Its Heisenberg's :grin: called the Heisenberg microscope.

http://en.wikipedia.org/wiki/Heisenberg%27s_microscope.

I don't think there is a need for measuring time.

I have modified to remove unwanted doubts that might arise off topic to what I am looking for. So i have not decided how the experiment is set up completely.

Elaborating a bit further,

If this experiment is 100% correct and since the uncertainty principle is one of the foremost pillar of quantum mechanics and since my modification adheres completely(?) without violating the original, I conclude either of 2 things

Say, momentum error is infinite and position x is completely determined
1. The speed of light is instantaneous. Then we can find the particle at time t. Because the photon reaches it instantly.
2. The position can only determined in a future 'd/c' which might be small, but finite.

sub note on 2 : So if we know that we are going to make an observation, we should desire to know after a time 'd/c' which will be the time at which the particle collides and instantaneous for our observation (in the future), which is what we want. Anyways, it is impossible to trace back to the particle's position.

One is known false. So that leaves 2. Which should give a relation relating to the lag and the probability of the particle being at a position d away from the source of the photon.
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Re: Impossibillity of measurement at time t

#5  Postby heisenbinker » Sep 02, 2011 10:12 am

twistor59 wrote:


If you're talking about a Heisenberg Microscope - type experiment, do you really need to worry about the time of the position observation ? Isn't it the case that we're just concerned with the uncertainty in the position ?


Yes, you are right but im trying to discuss an implication. I get your point though. The Heisenberg microscope is the most basic microscopic experiment for observation ive come across, so i used it. Are there any other experiments(of quantum nature) to calculate a quantity instantly?
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Re: Impossibillity of measurement at time t

#6  Postby twistor59 » Sep 02, 2011 11:48 am

heisenbinker wrote:
twistor59 wrote:


If you're talking about a Heisenberg Microscope - type experiment, do you really need to worry about the time of the position observation ? Isn't it the case that we're just concerned with the uncertainty in the position ?


Yes, you are right but im trying to discuss an implication. I get your point though. The Heisenberg microscope is the most basic microscopic experiment for observation ive come across, so i used it. Are there any other experiments(of quantum nature) to calculate a quantity instantly?


The problem with "instantly" is that you always run into the energy-time uncertainty relation. Although it's not a fundamental relation like the position/momentum uncertainty, the inequality nevertheless holds true i.e. you have this Δt on the measurement time. Lot's of discussion here
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Re: Impossibillity of measurement at time t

#7  Postby heisenbinker » Sep 03, 2011 9:52 am


twistor59 wrote:
The problem with "instantly" is that you always run into the energy-time uncertainty relation. Although it's not a fundamental relation like the position/momentum uncertainty, the inequality nevertheless holds true i.e. you have this Δt on the measurement time. Lot's of discussion here


Very interesting read. Thanks.
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Re: Impossibillity of measurement at time t

#8  Postby cavarka9 » Sep 03, 2011 6:42 pm

twistor59 wrote:
heisenbinker wrote:
twistor59 wrote:


If you're talking about a Heisenberg Microscope - type experiment, do you really need to worry about the time of the position observation ? Isn't it the case that we're just concerned with the uncertainty in the position ?


Yes, you are right but im trying to discuss an implication. I get your point though. The Heisenberg microscope is the most basic microscopic experiment for observation ive come across, so i used it. Are there any other experiments(of quantum nature) to calculate a quantity instantly?


The problem with "instantly" is that you always run into the energy-time uncertainty relation. Although it's not a fundamental relation like the position/momentum uncertainty, the inequality nevertheless holds true i.e. you have this Δt on the measurement time. Lot's of discussion here


Thats really nice.
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