# Uncertainty and the speed of light?

• Sandeep T S
In summary, the uncertainty principle states that it is impossible to know the position and momentum of a particle exactly at the same time. This applies to ensembles of particles, not individual measurements. If there was a way to determine the position and momentum of a single particle with arbitrary precision, it would violate the uncertainty principle for an ensemble as well. The uncertainty principle is based on the probability distribution of measurements and does not apply to a single measurement.

#### Sandeep T S

By Uncertainty Principle speed of a particle cannot be constant. then speed of a single photon not?

Sandeep T S said:
By Uncertainty Principle speed of a particle cannot be constant
No. I am not sure how you came up with this, so I don’t know how to address it.

• willem2
Sandeep T S said:
By Uncertainty Principle speed of a particle cannot be constant. then speed of a single photon not?
According to uncertainty principle it's impossible to know the position and the momentum of a particle exactly simultaneously. The product of the uncertainties is >
ħ/2. If you would exactly know one of them, the uncertainty in the other must be infinite, which isn't possible. (If you detect a particle at all, you must have some idea where it is).
For particles not moving at the speed of light, the speed depends on the momentum, and if you knew the exact speed, you would know the exact momentum, and you would know nothing about the position at all, which is impossible.
However photons can have different momenta, even if they all move at the same speed, so there is no problem.

• Dale
willem2 said:
According to uncertainty principle it's impossible to know the position and the momentum of a particle exactly simultaneously.

That is untrue. It is a statement about ensembles of systems, not about individual particles.

That is untrue. It is a statement about ensembles of systems, not about individual particles.

If there was a way to determine the position and momentum of a single particle with arbitrary precision, it would violate it for an ensemble as well. Just repeat.
In a statement like σx σp >= ħ/2 we're talking about a probability distribution for the position and momentum of a single particle.

willem2 said:
If there was a way to determine the position and momentum of a single particle with arbitrary precision, it would violate it for an ensemble as well. Just repeat.
I can measure the position of a particle with arbitrary precision and I can measure the momentum of a particle with arbitrary position, but this does not allow me to do the same for an ensemble. When I perform my arbitrarily precise measurements on each member of the ensemble, I will find that the results are distributed according to the uncertainty principle. As an extreme example, I can first measure the momentum of every particle in the ensemble and then discard those whose momentum does not fall in a specified and arbitrarily narrow range; this is a preparation procedure for an ensemble of particles with known momentum. Now nothing stops me from measuring their position; but I will find a spread of position values consistent with the uncertainty principle.
In a statement like σx σp >= ħ/2 we're talking about a probability distribution for the position and momentum of a single particle.
Talking about the probability distribution of a single measurement is like talking about the probability distribution of a single sample. Analogously, when I state that a tossed coin is biased to come up heads 60% of the time, I'm not saying anything about anyone toss, I'm making a claim about the ratio of heads to tails in a hypothetical ensemble of identically prepared coins.

• Dale
Nugatory said:
I can measure the position of a particle with arbitrary precision and I can measure the momentum of a particle with arbitrary position, but this does not allow me to do the same for an ensemble. When I perform my arbitrarily precise measurements on each member of the ensemble, I will find that the results are distributed according to the uncertainty principle. As an extreme example, I can first measure the momentum of every particle in the ensemble and then discard those whose momentum does not fall in a specified and arbitrarily narrow range; this is a preparation procedure for an ensemble of particles with known momentum. Now nothing stops me from measuring their position; but I will find a spread of position values consistent with the uncertainty principle.
But you're assuming in your example that the uncertainty principle applies to each particle. @willem2, I believe, is saying if the uncertainty principle doesn't apply to a single particle, as Vanadium implied, then you can determine the momentum and position of the particle to arbitrary precision at the same time. So to repeat your example, do this for a bunch of particles, discarding the ones that don't fall in the arbitrarily narrow ranges of position and momentum at the same time. You now know the momentum and position of the ensemble precisely.

Nugatory said:
Talking about the probability distribution of a single measurement is like talking about the probability distribution of a single sample. Analogously, when I state that a tossed coin is biased to come up heads 60% of the time, I'm not saying anything about anyone toss, I'm making a claim about the ratio of heads to tails in a hypothetical ensemble of identically prepared coins.
You could also repeat the measurement multiple times with the same coin, and the underlying probability distribution will emerge.

From my understanding, the uncertainty principle does apply to a single particle. If the particle is in some state, you can calculate ##\Delta x## and ##\Delta p## based on that state, and the product of those two quantities will be greater than ##\hbar/2##. It has nothing to do with making measurements. It has to do with the waviness of nature at the quantum level.

vela said:
If the particle is in some state, you can calculate ##\Delta x## and ##\Delta p## based on that state, and the product of those two quantities will be greater than ##\hbar/2##. It has nothing to do with making measurements. It has to do with the waviness of nature at the quantum level.
My understanding is that ##\Delta x## is a measure of the spread of position measurements on an ensemble of particles all in that state. Similarly, ##\Delta p## is the spread of momentum measurements made on a similarly prepared ensemble. Their product is a property of the state (and thus the ensemble).

(I'm essentially agreeing with the post by @Nugatory above.)

vela said:
But you're assuming in your example that the uncertainty principle applies to each particle.
That is not how I read his comment. To me it seems that he is talking about arbitrarily high precision for the position and momentum of a single particle.

Dale said:
That is not how I read his comment. To me it seems that he is talking about arbitrarily high precision for the position and momentum of a single particle.
Simultaneously?

vela said:
Simultaneously?
Yes

A photon can have a fairly precise momentum (to the extent that you can accurately determine its wavelength), but it can't be "localized" in a way that's compatible with the usual formulation of the Heisenberg Uncertainty Principle. The principle does apply, but the mathematics are different for massless particles. Nice summary here: https://arxiv.org/abs/1205.0516

## 1. What is the uncertainty principle?

The uncertainty principle is a fundamental principle in quantum mechanics that states that the more precisely you measure one property of a particle, the less precisely you can know about another related property. In other words, the more you know about a particle's position, the less you know about its momentum, and vice versa. This principle applies to all particles, including photons (which make up light).

## 2. How does the uncertainty principle relate to the speed of light?

The uncertainty principle is directly related to the speed of light through the concept of energy and mass. According to Einstein's famous equation, E=mc², energy and mass are equivalent and can be converted into each other. Since photons have no mass, they must have energy in order to exist. This energy manifests as their speed, which is always constant at the speed of light. Therefore, the more precisely we know the energy (and thus the speed) of a photon, the less we know about its position.

## 3. What is the speed of light in a vacuum?

The speed of light in a vacuum is approximately 299,792,458 meters per second, or about 670 million miles per hour. This is the fastest speed at which anything in the universe can travel, and it is a fundamental constant of nature. It is denoted by the letter "c" and is used in many equations in physics, including those that describe the behavior of light.

## 4. Can the speed of light ever be exceeded?

No, the speed of light cannot be exceeded. It is the maximum speed at which energy, information, or matter can travel in the universe. While there have been some theories and experiments that suggest the possibility of faster-than-light travel, none have been proven or accepted by the scientific community. The speed of light is a fundamental limit that is deeply ingrained in the laws of physics.

## 5. How do scientists measure the speed of light?

Scientists use various methods to measure the speed of light, including timing how long it takes for light to travel a known distance, using interference patterns to calculate the speed of light in a medium, and using the principles of special relativity to measure the speed of light in a moving reference frame. One of the most accurate methods involves using lasers and mirrors to create a precise beam of light that can be measured using sophisticated equipment.