This always confuses me and I’m not sure how it works. Please explain…
In: 252
[removed]
In a sense, we don’t really know why. We merely notice that it seems impossible.
Not just in practice (e.g. if you look at it, that means striking it with light and watching the reflection, which would push it around), but mathematically in principle our theories can’t even imagine a way to measure both.
You might wonder, ‘why not develope a better theory’? Well, the theories have to agree with all our current experimental results, and the weird world of Quantum Mechanics seems to force us to adopt a theory with features like the “Uncertainty Principle”, which in turn leads to the inability to know the speed & position of something to high precision.
–
Note that the Uncertainty Principle in this case is that we cannot know **both** *to arbitrarily high precision* at **the same time**. We can measure both, but at each moment the measurements will share between them some uncertainty.
For instance, in-principle, maybe we can get:
* a decent estimate of both position and velocity
* a great estimate of position, and a bad estimate of velocity
* a great estimate of velocity, and a bad estimate of position
* absolute 100% certainty of position, but total 100% ignorance of velocity
* absolute 100% certainy of velocity, but total 100% ignorance of position
For instance, in simple Quantum Mechanics practice problems, we sometiems deal with a perfect ‘plane wave’ of an electron. This sort of toy-idea of an Electon’s Wavefunction lets us easily read-off the velocity*, there is essentially a nubmer that tells us exactly what it is. However, this toy-idea of a wavefunction is spread out equally across the whole universe, so we forefeit literally any clue as to where it is.
In such examples, it turns out that if we want to be accurate at predicting quantum behaviour, the *only* ways that we know to successfully describe an electron is to resort to using something like a wavefunction, and any wavefunction (or similar) we use to describe it will have one of the uncertanities above. It isn’t just part of our measurement-method, but part of how the wavefunctions behave.
And, like I mentioned earlier, we can’t just use a ‘better’ wavefunction without these features, because then they don’t work (they don’t help us predict the results of experiments).
[* technically it is ‘momnetum’ rather than ‘velocity’, but that isn’t too important a differnece].
One of the best explanations I’ve seen, while not *100%* accurate, gets the point across decently well and intuitively.
Imagine you’re taking a picture of a car speeding past you, and you only have time to take one picture. You can use a slow shutter speed, in which case the car will be “smeared out” by its motion blur. You could then determine roughly how fast the car was moving based on the length of the blur, but it’s a bit difficult to say where exactly the car is since it’s so blurry.
Or, you could use a fast shutter speed, giving you a nice, crisp picture of the car with no motion blur. Now, you know exactly where the car is, but you can’t really tell how fast it’s moving. You could try somewhere in the middle, but there’s a fundamental limit to how precise you can be with the two measurements. That’s the Uncertainty Principle.
A similar thing happens when trying to measure electrons, you either get a well-defined point that’s easy to pinpoint but difficult to say how fast it’s moving, or you get a smeared-out blur that you can get a speed from, but it’s difficult to determine where it is. Things get even messier when you throw in wave-particle duality, quantum mechanics, and other ways that physics doesn’t behave as expected on such small scales.
The more concentrated a wave is in one spot, the harder it is to define what its frequency is. And the easier it is to define its frequency, the more spread out the wave is. That’s it. It’s a basic mathematical property of waves.
People really overthink this one and sometimes view it as something almost mystical, but it’s incredibly simple and almost obvious.
Certainties of measurement. HOw does one measure these things? Usually its a calculation, as physical measurement is limited to the accuracy of the equipment. If you measure electrical frequency with ans Oscilloscope, watch the waveforms as frquency increases, iit will depend on the accuracy of the transidtors, rectifiers and general componants used to manufacture the machine, and accuracy of calibration. I did City and Guilds in Electronics thirty years ago, and equipment is better now than then, but basic theories seem to have little change.
Ely5?
Easy. We don’t know why.. That’s just what the maths tell us.
My, admittedly limited, understanding is that we CAN know both of a particular something. It’s just one or the other will have very spread out distributions on repeated experiments. Put another way, if you have an experiment that sends out an electron you can’t precisely predict both the position and momentum of said electron (more precisely, the product of your standard deviation of both has a lower bound). However when you actually do the experiment and an electron does come out, the principle doesn’t stop you from measuring it.
I think explanations are best left to people who actually understand better; I recommend [this video by Sabine Hossenfelder](https://www.youtube.com/watch?v=qC0UWxgyDD0). However I’ll try to do my best below, if only to get some feedback and corrections on my own understanding.
The spread out distribution bit is a property of waves in general. For the extremes think about how a single frequency is just a sin wave that keeps waving across all time while say a unit pulse in frequency domain contains every frequency. For the middle, I think it’s easiest to bust out your favorite graphing calculator/software and plot the sum of sin(nx)/(nx) with n from 1 to increasingly large numbers. You should see that with more and more frequency you can constrain your signal tighter and tighter in time.
After that, we need to relate certain pairs of property to time and frequency distribution. For example, energy of photons is plancks constant * frequency. So now all of a sudden a wide distribution in frequency results in a wide distribution in energy of, say, photons shooting out of something. However the energy of a particular photon can still be known.
It is a confusing concept, but here is how I think of it. Velocity is the change in position over time – to measure the speed of a car, you have to know where it is at time 1, then time 2. We do this with a car by counting the turns of the wheels – it turns x rotations a second, the wheel has a diameter of y, so it is going xy per second. If you stop the car to check the wheel’s position, can you know how fast it was going? By definition, speed requires that the thing whose speed you are measuring is changing position – and every time it changes position, it’s speed can change – so at some level of super accurate precision, even for a car, you cannot know both its position and its velocity. An electron is so small that everything about it is at a supremely high level of precision.
I realize that probably is not the explanation- but that’s how I think about it. The physicists can now commence downvoting.
Speed is what happens between two points.
When people say “your car was driving 50 km/h at this point on the road” what they mean is that while passing from a point before the spot you were measuring at, to a point behind the spot you were measuring at, you moved with a speed of 50 km/h.
There is no speed in one single point; you’re at that point, nowhere else, otherwise you couldn’t have been seen there. Speed is how fast you arrived and left at the point that was being measured.
simple answer is “there is no speed and position of the electron”. there is only a probability of the position or velocity of a certain “quantized value” of the energy type, which is a wave (its true form).
I am leaning more towards the Everett interpretation of the wave function still.
In this interpretation, there is no “particles”. All energy is simply “waves”. when waves interact they produce quantized (or fixed) values with an apparent geometry due to our perception. “Particles are a specific energy value with a specific “spin” producing a “spherical geometry”.
Latest Answers