Should the speed of light be slightly uncertain?

[g.lemaitre]

The position and momentum of a photon is uncertain. If that is the case, then shouldn't the speed of light be slight uncertain?

 

[strangerep]

The position and momentum of a photon is uncertain. If that is the case, then shouldn't the speed of light be slight uncertain?

Have you ever tried to construct a good position operator for the photon in the relativistic context? Afaik, no one has done it in a fully satisfactory way.

 

[Integral]

We do not need to measure the location of a photon when finding the speed of light.

Read this about the definition of the meter.

By definition the speed of light is an integer, therefore no uncertinatiy

 

[g.lemaitre]

Read this about the definition of the meter.

By definition the speed of light is an integer, therefore no uncertinatiy

Don't know what you mean by integer. Also didn't understand why you wanted me to read the wiki article on meter.

 

[Integral]

Because you have to read to learn. NOW READ IT.

 

[g.lemaitre]

I read it before you advised me to read it of course and I still don't understand what you're getting at. If what you're getting at is the speed of light is relative to the observer, well, I already know that but I still don't see why it's speed cannot be uncertain.

 

[Integral]

If you had read all of it you would know why the speed of light is an integer.

 

[g.lemaitre]

Never mind, I give up

 

[Dale]

Never mind, I give up

After 2 hours and 40 minutes. Really?

c is a defined constant, as such its uncertainty is 0. What is uncertain is the length of a meter. That is the point to take from the reading.

 

[g.lemaitre]

After 2 hours and 40 minutes. Really?

c is a defined constant, as such its uncertainty is 0. What is uncertain is the length of a meter. That is the point to take from the reading.

Thanks. I appreciate your help.

 

[Chopin]

My god, you guys, what a bunch of rude and pointless arguing of semantics you're giving out here! Those answers completely ignore the intent of the question. I have no idea what you were trying to accomplish with that.

g.lemaitre: The speed of light is a consequence of relativity, not of quantum mechanics, so the types of uncertainty that pop up in studies of quantum behavior don't really apply to it. Lorentz invariance implies that there is a maximum speed that things asymptotically tend towards as you try to accelerate them, and the principles of Quantum Field Theory tell you that a massless particle can't propagate at any velocity except for that speed, so the speed of light is thus completely fixed.

 

[Integral]

I will spoon feed you some more. From the article I was trying to get you to read.

Speed of light
To further reduce uncertainty, the seventeenth CGPM in 1983 replaced the definition of the metre with its current definition, thus fixing the length of the metre in terms of the second and the speed of light:
The metre is the length of the path traveled by light in vacuum during a time interval of 1⁄299,792,458 of a second.[2]
This definition fixed the speed of light in vacuum at exactly 299,792,458 metres per second.

 

[Integral]

My god, you guys, what a bunch of rude and pointless arguing of semantics you're giving out here! Those answers completely ignore the intent of the question. I have no idea what you were trying to accomplish with that.

g.lemaitre: The speed of light is a consequence of relativity, not of quantum mechanics, so the types of uncertainty that pop up in studies of quantum behavior don't really apply to it. Lorentz invariance implies that there is a maximum speed that things asymptotically tend towards as you try to accelerate them, and the principles of Quantum Field Theory tell you that a massless particle can't propagate at any velocity except for that speed, so the speed of light is thus completely fixed.

This is a bit backwards, Relativity is a consequence of the constancy of the speed of light. The constancy of the speed of light is due to the nature of the universe. Lorentz invariance was COOKED to model the constancy of the speed of light. So naturally it has a max speed.

 

[Chopin]

I will spoon feed you some more. From the article I was trying to get you to read.

Except that that wasn't at all what the question was asking. The question was: since the Heisenberg Uncertainty principle limits our ability to simultaneously know the position and momentum of a particle, is it possible EVEN IN PRINCIPLE to know the speed of light exactly? A satisfactory answer to that question must involve some reference to the physics of relativity and quantum mechanics, not a history lesson.

 

[Chopin]

This is a bit backwards, Relativity is a consequence of the constancy of the speed of light. The constancy of the speed of light is due to the nature of the universe. Lorentz invariance was COOKED to model the constancy of the speed of light. So naturally it has a max speed.

Right, except for one detail. Lorentz invariance implies there is a maximum speed that anything can go, but it doesn't necessarily tell you that light must go at that speed. In order to show that, you have to use Quantum Field Theory, where you show that massless particles have four-momenta with magnitude zero, meaning that they travel at exactly that top speed. Then Lorentz invariance tells you that they must travel at that speed in all frames of reference.

 

[Integral]

Seems to me in post #10 the OP was happy with the being spoon fed the contends of the article I pointed him at. So maybe he really didn't understand his original question as well as you do.

My entire effort was pointed at getting the OP to think for himself just a bit.

 

[Crazymechanic]

Well the easy way of telling this maybe would be that yes we don't know the exact position of a particle but the speed of light doesn't depend on this one particle to measure , we can just have a beam of light from one point traveling down a certain distance (assume a large one as the speed is very high ) and then take a measurement on a very precise clock to see how many "ticks" or "vibrations" of an cesium atom (in a atomic clock) have passed.
Now the rest is elementary maths so remember that we have measured light speed on the macro scale and to do that doesn't require to know where a particular photon is at a given time as they usually come many not one.

 

[Naty1]

Saying that we now DEFINE light to have a certain 'exact' speed doesn't really address whether it HAS that speed or not, and if it does, can we measure it...'exactly'...

OP:

The position and momentum of a photon is uncertain. If that is the case, then shouldn't the speed of light be slight uncertain?

Why do you think it is 'uncertain' ??

"particles" may have well-defined positions and momentum at all times, or they may not ... the statistical interpretation of QM does not require one condition or the other to be true... Quantum mechanics doesn't say whether or not a particle has a position and a momentum at all times.

from the current discussion...

... since the Heisenberg Uncertainty principle limits our ability to simultaneously know the position and momentum of a particle, is it possible EVEN IN PRINCIPLE to know the speed of light exactly?

first part: Well, as has been discussed in numerous threads in these forums, that is NOT what HUP says...just briefly from those discussions:

In quantum mechanics, measurement of observables exhibits some seemingly unintuitive properties. Specifically, if a system is in a state described by a vector in a Hilbert space, the measurement process affects the state in a non-deterministic, but statistically predictable way. After a measurement is applied, the state description by a single vector may be destroyed, being replaced by a statistical ensemble.

In quantum mechanics, the Schrödinger equation, which describes the continuous time evolution of a system's wave function, is deterministic. However, the relationship between a system's wave function and the observable properties of the system appears to be non-deterministic…. A deterministic model will thus always produce the same output from a given starting condition or initial state...

Is it possible to simultaneously measure the position and momentum of a single particle. The HUP doesn't say anything about whether you can measure both in a single measurement at the same time. That is a separate issue.

It is possible to measure position and momentum simultaneously…a single measurement of a particle. What we can't do is to prepare an identical set of states…. such that we would be able to make an accurate prediction about what the result of a position measurement would be and an accurate prediction about what the result of a momentum measurement would be….for an ensemble of measurements...

One of the lengthy discussions is here:

https://www.physicsforums.com/showthread.php?t=516224


Note there are likely conflicting viewpoints along the way...so read along before getting 'all fired up' [lol]

One explanation I heard was that if you, say, bounced a photon off an atom to measure its position, then the recoil would affect its momentum, thus giving rise to the uncertainty - this seems straightforward enough. However, I have also been told that this is apparently not a valid explanation, although I do not understand why.

And of course this IS an issue, but has nothing to do with HUP...this is a problem with measurement apparatus.


Another discussion is here:

Do particles have well defined positions at all times
https://www.physicsforums.com/showthread.php?t=499976

But BEWARE: THE BALLENTINE paper seems to draw some questionable conclusions!

 

[Naty1]

I forgot to post:

http://en.wikipedia.org/wiki/Speed_of_light#Measurement

...doesn't seem like photons are routinely used to 'measure the speed of light' anyway...edit: so to answer the original question, it seems like we are limited only via our ingenuity in developing ever more accurate measurement devices.

 

[phinds]

... My entire effort was pointed at getting the OP to think for himself just a bit.

And you did it in a way that I think reflects how good this forum is, that you take the time to figure out what might be helpful to an OP and you nudge him/her towards it. It's hardly your fault that some people resist nudging and thinking.

 

[BWV]

even in a naive model of measuring photons with a hypothetical absolutely precise speed detector the UP is inconsequential

after 1 second light would have traveled 300 million meters & the uncertainty of the speed clocked for the photon would have a standard deviation of 10^-34 meters / second, so even say a 10 sigma error would be immaterial

 

[russ_watters]

For a question of what the HUP has to say about the speed of light, you should read an article on the HUP, not on SR. The wiki on the HUP has a section on this that does indeed confirm that it applies to photons/the speed of light.

 

[fluidistic]

For a question of what the HUP has to say about the speed of light, you should read an article on the HUP, not on SR. The wiki on the HUP has a section on this that does indeed confirm that it applies to photons/the speed of light.

I'd appreciate the section... I'm reading through it (http://en.wikipedia.org/wiki/Uncertainty_principle) but I don't see where they talk about the speed of light.
The question of the OP blows my mind. I don't understand how it's possible to have an uncertainty in the position but not in the velocity, if I consider that the velocity is the derivative of the position with respect to time.

 

[russ_watters]

I'm on a cell phone at the moment and can't easily post quotes: it is the section on critical reactions, several subsections, but the one on Einstein's box in particular. Last sentence says position uncertainty applies to photons.

 

[Physics Monkey]

Here is a little concrete calculation that has some bearing on what I interpreted the OPs question to be.

Consider a relativistic quantum particle of mass $m$. Let its position be $\vec{x}$ and its momentum be $\vec{p}$. We may write a formula for the velocity of the particle which reads
$$\vec{v} = \frac{\vec{p}}{\sqrt{p^2 + m^2}}$$
in units where the "speed of light" (i.e. a unit conversion factor) is one.

Certainly the following things are true for this particle. Unless the particle is in a momentum eigenstate, the velocity of the particle is uncertain. If we prepare the particle in a localized wavepacket, then the momentum uncertainty and hence also the velocity uncertain will be related to the localization in position. However, there is a curious feature here since the velocity is a bounded operator.

To see something interesting, consider a Gaussian wavepacket with $\langle p \rangle \rightarrow \infty$, but with a fixed variance $\delta x^2$. When acting on high momentum states, the "speed squared" operator may be expanded as
$$\vec{v} \cdot \vec{v} = 1 - \frac{m^2}{p^2}+ ...$$
The variance of this speed squared operator is
$$\Delta \equiv \langle (v^2)^2 \rangle - \langle v^2 \rangle^2 .$$
Now I think the following is true (and I have checked it in a simplified wavefunction), the variance $\Delta$ vanishes as $\langle p \rangle \rightarrow \infty$ at fixed $\delta x^2$. Hence we may take a limit by first sending $\langle p \rangle \rightarrow \infty$ to obtain a particle moving at the "speed of light" with no variance in its "speed squared" operator. We may then adjust $\delta x^2$ to localize the particle as we see fit. So here it seems we obtain something like a particle with the usual position-momentum uncertainty but with definite speed, the "speed of light", in a certain limit.

Now I know there are many issues with relativistic position operators and so forth, but perhaps this little calculation will be somewhat helpful.

 

[Physics Monkey]

A further note. One can achieve the same limit by sending $m \rightarrow 0$ instead of $\langle p \rangle \rightarrow \infty$. One still obtains a speed square operator approaching one with no variance, yet the direction of the velocity remains a fluctuating variable.

Also, such considerations may not be totally academic since we have materials, e.g. graphene, in which under certain circumstances ordinary electrons behave like massless relativistic particles.

 

[Crazymechanic]

Now forgive me if i somehow get too philosophical on this but after what everyone here said I was especially struck after reading @fluidistic post , quite simply put that you have a blown mind after this...
Well your right if we don't know the position but know the speed then the only way the speed is right is to assume that the photon can be in multiple points at once but that doesn't sound right.

The HUP basically states that from two variables at a given time you can be sure of only one.
In the case of particle position to which it originally refers to either you know the position and the speed is left uncertain or the speed and then the position is "blurred"
Now I'm sure we have had plenty of discussion here about that but to me it seems that either we have gotten wrong the upper limit of speed in the universe (seems unlikely) or we just have a shortcoming in measuring and or calculating the position of a particle together with it's speed.
As to a single particle following it's trajectory with no matter what speed can take only one place at a time it should logically be so.
Now there are many explanations of why HUP is the way it is but does anyone know of a proven explanation of why things are like that except from the skeptic viewpoint that it is rather our lack of knowledge of the particles position , although I think the mainstream interpretation accepts the HUP as a phenomenon of QM basically.

 

[Naty1]

The question of the OP blows my mind. I don't understand how it's possible to have an uncertainty in the position but not in the velocity, if I consider that the velocity is the derivative of the position with respect to time.

velocity as the derivative of position wrp to time is a low speed approximation.

If it were accurate at high speeds, we could accelerate things to light speed. In other words, V_total= V₁ plus V₂ is an approximation...

Proper acceleration is the rate of change of RAPIDITY with respect to proper time.

http://en.wikipedia.org/wiki/Velocity-addition_formula Velocities add as explained here:

http://en.wikipedia.org/wiki/Special_relativity#Composition_of_velocities

 

[Naty1]

The Wikipedia article on HUP can be extremely misleading although they do get some basics correct.

Here is one of the clearest descriptions of what the HUP is and what it is not...
[my boldface for emphasis]

PAllen: If you are measuring position and momentum of the 'same thing' at two different times, the measurements are necessarily timelike. The measurements occur at two times on the world line of the thing measured. This order will never change, no matter what the motion of the observer is. If, instead, they occur for the same time on the "thing's" world line, they are simultaneous for the purposes of the uncertainty principle.


To measure a particle's momentum, we need to interact with it via a detector, which localizes the particle. So we actually do a position measurement (to arbitrary precision). Then we calculate the momentum, which requires that we know something else about the position of the particle at an earlier time (perhaps we passed it through a narrow slit). Both of those position measurements, and the measurement of the time interval, can be done to arbitrary precision, so we can calculate the momentum to arbitrary precision. From this you can see that in principle, there is no limitation on how precisely we can measure the momentum and position of a single particle.

Where the HUP comes into play is that if you then repeat the same sequence of arbitrarily precise measurements on a large numbers of identically prepared particles (i.e. particles with the same wave function, or equivalently particles sampled from the same probability distribution), you will find that your momentum measurements are not all identical, but rather form a probability distribution of possible values for the momentum. The width of this measured momentum distribution for many particles is what is limited by the HUP. In other words, the HUP says that the product of the widths of your measured momentum probability distribution, and the position probability distribution associated with your initial wave function, can be no smaller than Planck's constant divided by 4 times pi.

Here is an analogous explanation, I believe from Albert Messiah's text QUANTUM MECHANICS
[again, my boldface]

Physical systems which have been subjected to the same state preparation will be similar in some of their properties but not all of them. ... So it is natural to assert that a quantum state represents an ensemble of similarly prepared systems, but does not provide a complete description of an individual system...For example, a single scattering experiment consists of shooting a single particle at a target and measuring its angle of scatter. Quantum theory does not deal with such an experiment but rather with the statistical distribution of the results of an ensemble of similar results... The wave function describes not a single scattering particle but an ensemble of similarly accelerated particles. Quantum theory predicts the statistical frequencies of the various angles through which a particle may be scattered.

 

[Naty1]

Here is a third [consistent] explanation:
ZapperZ explains HUP in is blog "Misconception of the Heisenberg Uncertainty Principle."http://physicsandphysicists.blogspot.com/2006/11/misconception-of-heisenberg-uncertainty.html“One of the common misconceptions about the Heisenberg Uncertainty Principle (HUP) is that it is the fault of our measurement accuracy. A description that is often used is the fact that ….a very short wavelength photon has a very high energy, and thus, the act of position measurement will simply destroy the accurate information of that electron's momentum.


While this is true,(about measurement limitations of equipment) it isn't really a manifestation of the HUP. The HUP isn't about a single measurement and what can be obtained out of that single measurement. It is about how well we can predict subsequent measurements given the ‘identical’ conditions...What I am trying to get across is that the HUP isn't about the knowledge of the conjugate observables of a single particle in a single measurement. I have shown that there's nothing to prevent anyone from knowing both the position and momentum of a [single] particle in a single measurement with arbitrary accuracy: that is limited only by our technology. However, physics involves the ability to make a dynamical model that allows us to predict when and where things are going to occur in the future. While classical mechanics does not prohibit us from making as accurate of a prediction as we want, QM does! It is this predictive ability that is contained in the HUP. It is an intrinsic part of the QM formulation and not just simply a "measurement" uncertainty, as often misunderstood by many.

 

[fluidistic]

velocity as the derivative of position wrp to time is a low speed approximation.

I didn't know this. What is the general relativistic relation then? Or the not approximated expression?

If it were accurate at high speeds, we could accelerate things to light speed.

Why? I really don't see the implication.

In other words, V_total= V₁ plus V₂ is an approximation...

I know this but I don't see how it relates to "v=dx/dt implies v=v_1+v_2".

About the quotes you posted on the HUP, in fact I think the problem is that we aren't making any measurement. Consider any photon, you know it's moving at a speed "c" without any uncertainty. You don't even need to make a measurement for that, else special relativity is violated.

So let's say I measure the position of a photon with a screen that reacts to photon by darkening or something like that. I'd have a finite uncertainty in the position and also in the momentum (the HUP is not violated), but apparently none in the velocity. I'm still puzzled on how to get no uncertainty in the speed (that ok, I did not measure since I know it no matter what) but I have an uncertainty in the position.

Edit: I think I'm starting to understand something. The HUP is not related -directly at least- to the speed of a photon but on its momentum and position. Unlike a massive particle, the momentum of the photon is not related to its speed so an uncertainty in its momentum does not imply an uncertainty in its speed. Instead, an uncertainty in position should raise an uncertainty in velocity, not necessarily speed.
Am I wrong if I think that it's possible to have an uncertainty in position and in velocity and no uncertainty in the speed at the same time?
This would solve the problem...

Basically you know how fast the photon is moving no matter what. You don't know "perfectly" its momentum nor its position, all this at the moment it hit your screen. However there's an uncertainty in the direction the photon when it hit the screen.
So to answer the OP, the HUP principle applied to a photon does not imply an uncertainty in speed. Instead, in the velocity due to the uncertainty associated to its position.
Does this make sense? This does to me.