# Are there limits to human/devices perception?

• DarkFalz
Each atom has an infinity of positions it could be in, so the analogy works.But space is continuous, right? So particles can have an infinity of positions, hence the analogy works. Am i correct?Yes, space is continuous. However, when you take a big enough sample, the positions of the particles will be close to each other.f

#### DarkFalz

As far as i know, measurement devices present measurements based on something that affects the device's particles, for instance, forces, heat, tension, voltage...

My question is, given that every change of position of any particle may affect the particles of the measurement device, why can't we design devices that can distinguish between any state of the universe?

Consider for instance our human body. If i have a car behind a Wall, i cannot distinguish this situation from one where there isn't a car behind the Wall, since i only see the Wall. Still, having a car behind the Wall surely affects something in our particles, maybe the gravity pull from the car, or some change in the overall environment light, or even a change in the trajectory of the light that arrives in our eyes (since we perceive light), even if the effect is minimal.

Is there some law that limits measument and devices so that we cannot have a device that can distinguish from every state of the universe?

Thanks in advance

I would compare this to trying hear one voice from all the voices in the world. The sounds would be so entangled that there'd be no way to pull out a clear signal from the noise.

Is there some law that limits measument and devices so that we cannot have a device that can distinguish from every state of the universe?

I'd say the limit depends on the sensitivity of our equipment. Detecting some things, such as very low frequency EM waves, is so difficult that the required measuring device becomes horribly impractical to build.

There's a basic problem that goes with all measurements and that is Noise. Random fluctuations are everywhere, due to temperature, grittiness of very small currents due to individual electrons being involved and other effects. Also there can be interfering signals from other sources. However 'sensitive' your equipment is -i.e. however much you can turn up the gain, there will be randomness. The wider the bandwidth (aka response time and good frequency response) the more noise gets in. To counter this, you can narrow the bandwidth, which means that you need to take longer and longer over your measurement (averaging out the noise) to reach the desired accuracy.
The idea that superman could hear someone crying "help" is daft because there would be millions of other people shouting and playing music and he would be hearing the individual air molecules hitting his eardrums. Same thing goes for detecting distant stars in the presence of background light and the heat of the light detector.

Taking long enough and using, say, very high power Radar, you could detect the car behind the wall - it's all down to Signal to Noise Ratio.

A device that could distinguish every possible state of the universe would itself have to have at least as many possible states as the universe has. Since such a device would necessarily be a subset of the universe then it would either have to be the universe or it would have to have fewer states than the universe. Therefore, any such device would be the universe.

A device that could distinguish every possible state of the universe would itself have to have at least as many possible states as the universe has. Since such a device would necessarily be a subset of the universe then it would either have to be the universe or it would have to have fewer states than the universe. Therefore, any such device would be the universe.

There are as many numbers between 0 and 1 as there are in the whole real number range. Why is it impossible??

There are as many numbers between 0 and 1 as there are in the whole real number range. Why is it impossible??

Because this is real life, not pure mathematics. Recording a state of a system requires another system to use a state to do the recording.

Because this is real life, not pure mathematics. Recording a state of a system requires another system to use a state to do the recording.
But space is continuous, right? So particles can have an infinity of positions, hence the analogy works. Am i correct?

Even with continuous space and continuous time, the possible states of a finite apparatus are still discrete.

Nobody has mentioned quantum mechanics yet. When the scale of things are small enough to be in "the quantum realm", then there are very definite limitations on what can be measured.

The quantum realm can be defined as the scale where things are so small that no measurement can be sensitive enough to observe Anyang without changing the thing observed.

Even with continuous space and continuous time, the possible states of a finite apparatus are still discrete.

How is that possible? Let's consider a device composed of two atoms. These could be any distance D ∈ ℝ apart from one another, even if some of these values represent unstable situations.

There are quantum limits and there are thermodynamic limits to the measurement. The thermodynamics limits come into play because by making a measurement, we are decreasing the entropy of the thing we are measuring. This must be accompanied by an increase in entropy in our measurement system or surroundings. We cannot measure the state of the entire universe because that would reduce the entropy of the universe, which is not allowed. Anytime you make a measurement, you have to entangle the system under measurement with something external to the system (such as a probe, detector, computer, yourself...).

DarkFalz, one of the first problems studied by almost all students of quantum mechanics is called the particle in a box. If you haven't yet, I suggest you study it.

In quantum mechanics, particles (such as atoms) do not have definite positions, so your classical view of a state does not apply. Rather, particles must occupy certain quantum states (or superpositions of them). For example, an electron in a hydrogen atom is only allowed to exist in certain orbitals. The distance between the electron and nucleus is indeterminate in any of the orbitals (every time you measure it you will get a different result, even if the "state" is the same) although you can define an average distance, which is only allowed to take on certain discrete values. (You can get other values by taking superpositions of orbital states, but this is ultimately limited by the size of the apparatus.)

Note that DaleSpam said "finite apparatus". Finite is the key word here. For a particle in a box, the larger the box, the more states are available for a given energy. It takes up to infinite energy to create a state of two atoms with infinitely precise positions.

DarkFalz, one of the first problems studied by almost all students of quantum mechanics is called the particle in a box. If you haven't yet, I suggest you study it.

In quantum mechanics, particles (such as atoms) do not have definite positions, so your classical view of a state does not apply. Rather, particles must occupy certain quantum states (or superpositions of them). For example, an electron in a hydrogen atom is only allowed to exist in certain orbitals. The distance between the electron and nucleus is indeterminate in any of the orbitals (every time you measure it you will get a different result, even if the "state" is the same) although you can define an average distance, which is only allowed to take on certain discrete values. (You can get other values by taking superpositions of orbital states, but this is ultimately limited by the size of the apparatus.)

Note that DaleSpam said "finite apparatus". Finite is the key word here. For a particle in a box, the larger the box, the more states are available for a given energy. It takes up to infinite energy to create a state of two atoms with infinitely precise positions.

What if the position of the whole atom itself in the universe represents the state?

What if the position of the whole atom itself in the universe represents the state?
Its position is not precisely defined in QM.

What if the position of the whole atom itself in the universe represents the state?
States are represented by wavefunctions. The position is an operator on the wavefunction, not the state itself.

Khashishi's comments above are right on. You should look into the particle in a box and the Bekenstein bound. Any measuring device would necessarily be finite, even if the universe were infinite.

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Let's wrap it up then.

A device can't perform infinitely precise measurements because that would require infinite energy, which we do not have. Hence, when two very similar lights arrive to our eyes (or a camera), these are interpreted as the same color because the measuring device has finite precision when analyzing light, therefore if the RGB red component of a red light is, for instance, 1.3443666346 or 1.344365677 it does not matter because both are interpreted as 1.34436 (5 decimal places for example). Is this correct?

What i find the most weird in all of this is how we humans kind of perform a "round" of our measurements, because looking at a rock with 100000000000 atoms and one with 100000000000 -1 atoms is definitely different, but still we perceive it as exactly the same!

The same goes with digital measurement devices. If a digital device displays the temperature as 35,59ºC (only has 2 decimal places) but the temperature is actually 35,595466ºC or 35,76575ºC, but appear as PRECISELY the same, even though both represent different states of the device's particles. Is it that the device does not actually display the same but we humans interpret it as the same? I mean, if the temprature is different, even though the device displays the same digits, something inside of it has to be different, it is hotter in one situation than the other, and that affects particles. Are we humans the reason why we can't perceive the different states?

In some cases it is a limitation on our measuring instruments. In some cases we cannot define the quantity that we are measuring precisely enough to make a precise measurement possible (for instance, time of death accurate to the microsecond). In some cases it goes deeper than that -- the quantity that we are trying to measure simply does not exist (for instance, the precise position of a sub-atomic particle between measurements).

I would put temperature into that final category. Temperature is a statistical measurement. Focus down to the very small and the very precise and it stops existing at all.

In my view, that's not a human failure. That's just the way things are.

Many times finite measurement precision it is also a result of how we sample and store the information. For example, a sensor may have theoretically infinite precision in the sense that it is an analog instrument outputting a voltage, but modern computers store information digitally. In sampling the sensor voltage, we can only do this to finite precision, often 16 bits, so any information that cannot be measured within the constraints of the given bit depth is lost.

DarkFalz, I think you are missing the point in your last post. It's not just the measurement device that is finite. The item under observation is also finite. Since the item itself is finite, it doesn't have exact values of certain observable values, even if you use an infinite measuring device.

A finite device can only have a finite number of possible states. So it could be used to completely measure the state of a system that has fewer

A finite device can only have a finite number of possible states. So it could be used to completely measure the state of a system that has fewer

Then we can fully measure something? All talk until now seemed to point to the opposite.

Yes, you can fully measure something simple and small, not the whole universe. Note that "fully measuring" a real system is not the same as what you might hope from classical mechanics. You are left with uncertainty about future measurements on a system even with a known state.

Yes, you can fully measure something simple and small, not the whole universe. Note that "fully measuring" a real system is not the same as what you might hope from classical mechanics. You are left with uncertainty about future measurements on a system even with a known state.

Then tell me something. When you or i look at something and perceive it with a given color, if the color changes just slightly, we won't perceive it. Is this because our eyes cannot precisely measure the color up to the decimal place where it changed (considering the color as a magnitude)? Also the same follows when looking at a rock with 100000000000000 atoms and a rock with 1000000000000000-1 atoms? Also, could a device be created that could accurately distinguish between both of these situations? Or are our human perceptions limited just because we have not yet evolved enough? Or is it simply impossible?

You are still missing the point. Color is a function of human perception, so it isn't a good example here. But consider wavelength, which is much easier to precisely define than color. We can measure wavelength of a beam of light by using a spectrometer. A real spectrometer has limited resolution which has to do with the quality of the optical components, the dispersion of the diffraction grating, and the resolution of the screen or camera. But even with an imaginary perfect spectrometer, we will always measure some spread in wavelengths in a beam of light, because the source of the beam has some line broadening effects. There is no such thing as a perfectly monochromatic light source.

Quantum mechanics is an inherently random model. Suppose a gas discharge lamp is giving off some light. Let's say we have a detector that can detect the wavelength of each photon that is captured by the detector. So we get a series: 555.34, 555.73, 555.43, 555.64... Now you say, that is due to noise in the detector. But what if I tell you that the detector has a noise level of 0.01. Then clearly this spread in measurements is not due to the detector. The spread in values is due to the source of the light.

How are you going to define an "exact" color of something whose color is constantly changing? Do you want to take an average over a long time? You can, in principle, tell me what the "exact" color is after an infinite amount of time has passed. But in a finite universe, you can't do that. It doesn't matter if your detector is perfect.

(On the other hand, counting n atoms versus n-1 atoms should be possible with a good device.)

When DaleSpam says we can "fully measure" something, he doesn't mean that we can measure exact values for observables. He means we can measure the full quantum state of something. (we can only do this with very small systems.) Since quantum mechanics is random, the same state doesn't mean it will give the same observable values after a measurement. It's random! It means that you will draw from the same distribution of random values. It's like rolling perfectly identical dice.

Dale
When DaleSpam says we can "fully measure" something, he doesn't mean that we can measure exact values for observables. He means we can measure the full quantum state of something. (we can only do this with very small systems.) Since quantum mechanics is random, the same state doesn't mean it will give the same observable values after a measurement. It's random! It means that you will draw from the same distribution of random values.
Yes. Well said.

Also the same follows when looking at a rock with 100000000000000 atoms and a rock with 1000000000000000-1 atoms?
In principle it is possible. A state with a definite number of identical particles is called a Fock state. Many experiments produce and measure Fock states.

I don't think that any such a large device has been built, and I am sure there would be many engineering hurdles, but in principle I don't see why it couldn't be built other than economics.