As I understand it, this is indeed a fundamental feature of the Planck length; The universe might have structure smaller than this, but we wouldn't be able to tell. So the Planck length is the shortest meaningful length, in that we would never be able to discern structure smaller than this.
So, doesn't that suggest there's a Planck length for time? So the distance between two points in space-time is sqrt(x^2 + y^2 + z^2 - ct). If you try to find the distance of a point in space at two different times, does the Plank length dictate some type of Plank interval?
That page says the Planck time is the time it takes for light in a vacuum to travel one Planck length. That doesn't imply it's the smallest interval, does it?
Insofar as you can only really measure time as the interval it takes for something to happen, and insofar as light's travel is the fastest process in the universe, and that the plank scale is the smallest distinguishable distance, it follows that the measurement of time across that smallest interval is the shortest interval that can be reliably measured.
Doesn't that imply that every process in the universe proceeds in lock-step? If two virtual particles were to randomly pop into existence, does the time between the first and second particle appearing have to happen in some whole multiple of Planck time?
To my understanding, Planck time describes a limit on sample rate, not frequency. That is, we can't perceive time at a finer grain than whole multiples of Planck time. But even starting with only integers, we can theorize and simulate floats. The speed of light is as arbitrary a scale as anything else when you're talking about absolutes, hence "it's all relative".
Virtual particles actually exist for less than a planck unit of time. I'm not a physicist and I'm having trouble finding a good clear reference, but this page mentions it (cmd-f 'less than') - http://abyss.uoregon.edu/~js/ast123/lectures/lec17.html
Well, if light (the fastest possible thing) takes this amount of time to travel the Planck length (the shortest possible thing), then does that not imply that nothing could possibly happen faster?
There is no reason to expect that Planck length is the literally the shortest possible length. I'm not aware of any theory that suggests that.
It's more accurate to talk about Planck scale and not think it as strict limit.
Planck scale is where the structure of spacetime itself becomes dominated by quantum effects and the structure of spacetime may start looking really strange. Strange theories like loop quantum gravity, causal sets, causal dynamical triangulation, fractal cosmology, etc. work at Planck scale. According to fractal cosmology spacetime is 2-dimensional in Planck scale and gradually becomes 4-dimensional in larger scales. Loop quantum gravity sees it as "foamy".
Planck scale is also the area where measuring distances (differentiating with different positions in space) becomes impossible.
I love these ideas, but they all assume that spacetime quanta, or nodes, or whatever the hell they are, can still communicate and/or change state in some way.
Which suggests internal structure of some kind.
I'm wary of any explanation that says "Well, it's just random", because randomness turns out to be a complicated process.
It's hard to imagine that some kind of prototypical base quantum would be inherently random just because.
I suppose it's possible. But it would be unexpected.
The operating energy of the LHC is around 15 orders of magnitude less than the Planck energy (if I worked it out correctly). Therefore we cannot directly probe Planck length scales.
Planck length, nor any other Planck unit isn't the "shortest/smallest" anything* at least it was never intended to be that.
These units are very useful in QM and as "constants" (not the best choice of words since Planck units intentionally ignore constant values to some extent) that can be used to describe a relativistic universe.
*You can use Planck Length/Time to put a lower limit on any possible wavelength that below it a wave cannot exist, other Planck units can also be in the ballpark of the smallest possible unit/quanta of various things in various theories.
The uncertainty principle states that the product of the standard deviation of the momentum and posisition of a particle is bounded from below by h/4pi, where h is the plank constant.
This means that, in order to probe small distances, we must have great uncertainty in the momentum invovled, which means that there must be a lot of kinetic energy in the system. As the distances we probe become smaller, we have an increasing amount of energy in a decreasing amount of space.
E=mc^2 tells us that energy and mass are interchangeable. Specifically, energy, like mass, causes gravity. In order to probe below the plank length, we would need to put so much gravity in so small a space that we would form a black hole. However, because we cannot observe the inside of a blackhole, this prevents us from observing anything smaller than the plank length.
> it’s the only length that can be derived from the constants c, G, and h without adding some arbitrary constant—so it may retain the same value in all reference frames, not subject to any Lorentz contraction. But the Planck length is derived from universal constants, so it must have the same value in all reference frames; it can’t change according to a Lorentz contraction.
The arbitrary constant is 1. How is 1 less arbitrary than 2, 42, or 3.14?
I don't get it - is it trying to say objects of Planck length wouldn't contract due to relativity? If so - why?
1 is the multiplicative identity, i.e. x * 1 = x, hence we can always leave out a "* 1" factor without changing things.
A different factor, like 2, is more arbitrary, since "* 2" can't be left out without changing the value.
You can make the claim that a "* 1" factor is lurking in there, but even from that perspective it's less arbitrary than "* 2", since we could claim that "* 2" also has a "* 1" lurking in it, and so on :)
I mostly meant - how is this proving that object of length 1 * planck length won't contract, and object of 2 * planck length will. And if it's not - how is the length special?
The idea that the Universe is this sort of discrete lattice always makes me suspect simulation.
I feel like true reality should not become grainy at some point, it feels like a mark of artificial origin.
I see some hints too, but that's probably because my mind is wired to be programmer :) So it's probably just a sort of confirmation bias.
However seeing the quantum effects like a version of compression, dark matter and dark energy which could be an ugly hack to stabilize matter and galaxies, the fractal self similarity of the universe is just too amusing to ignore :)
Or you can simply think of it as the best "resolution" that macroscopic instruments rooted in 3 dimensions can reduce it to.
I feel like the whole "wave-particle duality" is already a hint that the true nature of reality may always remain outside of our observation capability.
In fact, I think that humans may be a little too biased towards picturing everything as made up of discrete parts ("particles"), and that is probably a byproduct of having visual eyesight. Can't wait to meet alien intelligences with completely different senses and see what they think. :)
QM can be defined by the fact that the reality you observe isn't the "actual reality", but overall it doesn't really matter.
Wave-particle duality is a bit of a misnomer it's more of a pop-sci concept, all particles are defined by their wave function and there isn't a "particle function".
And if you think that we are too biased towards picturing everything made out of discrete parts then you won't like QM which is basically what the Q stands for which is "quanta" as in the smallest clump-thing-w/e of something.
That said most people that choose to study physics in high school (year 10-12) and or college would be exposed to Quantum Field Theory which makes everything make considerably more sense when you start thinking about everything in terms of fields.
Once you no longer think of an electron as an individual thing but as a electron field that extends through all space and the particles are the quanta of that field as in localized excitations of the field which when they reach a certain amplitude or energy level bring forth something we can measure and identify as an electron.
I wish QFT would be popularized more because it would bring so many important concepts into the common sense realm and it would actually be easier to explain things like why do particle accelerators work.
I read about this phenomenon where the two slit experiment could be replicated with drops bouncing on an oil bath (here's an article on it: http://resonance.is/news/quantum-weirdness-replaced-by-class... ). And one about how a higher-dimensional mathematical object could dramatically simplify certain quantum mechanical calculation ( http://www.wired.com/2013/12/amplituhedron-jewel-quantum-phy... ). I realize this proves nothing, but I'm still holding out hope that the randomness we observe is just a result of the interaction that higher dimensional "matter/energy" does when it intersects with our 3/4 dimensions. Maybe god doesn't play dice after all, maybe there's just a whole lot going on before we get to make our measurements.
I think that gets it backwards: the universe can move information around and perform computation because it has a level where things become both discrete and stochastic.
FWIW, my own intuition it precisely the opposite. I would be very surprised if reality turned out to be continuous, because of the resulting infinite information density.
If the Planck length is Lorentz-invariant but macro-scale objects are not then does that not imply there is a special universal reference frame against which to measure velocity?
If I have understood the article correctly one would be able to measure the length of a spaceship relative to the Planck length and deduce velocity, entirely locally (i.e. onboard the spaceship).
This is a fundamental departure from general relativity which says there is no special frame of reference.
I guess this is simply one of the many incompatibilities between quantum theory and general relativity.
There are many attempts to combine these theories into a universal theory (pun intended), but it is hard to check the corner cases where those theories differ. That's one of the reasons we build better and better particle accelerators.
Either way, it doesn't make sense to apply (pure) general relativity to the small scale, nor to apply (pure) quantum theory to the large scale. The physicists know for decades about of that issue and are already taking care of that.
Quantum Gravity is pretty coherent it can explain the universe we see today, it can explain why an apple drops, and it can explain why galaxies form, it cannot explain the big bang and some periods after it but neither can general relativity.
For the most part particle accelerators are not needed to explain quantum gravity, we do use them to find "new physics" but this new physics is more in the lines of the known unknowns.
We also do apply relativity to small scales every day, without relativity muons could not be discovered and without relativity to some extent even large particle accelerators would not "work" because the effects of spatial contractions are pretty important for how we predict and analyse the data coming from particle accelerators especially the "messy kind" like the LHC.
As for the large scale stuff as mentioned earlier quantum gravity is pretty compatible with general relativity in terms of explaining how the universe that we see today looks and works, you can easily explain why and how the moon rotates around the earth, it does rely on a massless spin-2 particle called a graviton which is yet to be "discovered" and it does break if the graviton would have a different spin (for example spin-0 graviton).
So I don't really understand the notion of why people still think that quantum gravity and general relativity aren't compatible to the extent of "what the fuck is going on", which is odd since afterall GR isn't 100% compatible with the Standard Model either, since GR is background independent and does not care about the particular state or shape of space-time while SM does.
From your long statement I read that you agree with my criticism that one should not use the plain quantum theory, mix it with the plain general relativity, and wonder why this leads to contradictions. Of course it does! If one wants a coherent model, one should use the Standard Model instead (or one if its variants).
Not sure at which point you disagree with my statement, though.
Depends on what you define as GR, there are classical and relativistic versions of Quantom Mechanics.
Each theory is useful for various things because each theory provides you with certain tools and perspectives that are useful for performing specific tasks.
At the end every theory is a set of laws and abstractions you use theories to change the perspective of how you look at things but these are often abstracts.
You can look at particles as particles, waves or fields it doesn't change reality but every one of these viewpoints comes with its unique benefits and you can chose between them depending on what benefits you most to for a specific task or a situation.
A bit of a quibble but Lorentz transforms are a consequence of Special Relatively, and therefore predate General Relativity. That is, the objection you are raising would apply to frames of reference without referring to General Relativity, just Special relativity.
This is some of the best pop-sci writing I've read in quite some time. Hat's off to Carl Frederick; itching to go read some of his science fiction now.
The article is based on a popular misconception: The Planck length is Lorentz invariant, so special relativity must break down at Planck length scales.
However this is wrong. The Planck length is the minimal length of a 4-vector (a 4-dimensional vector measuring the distance between two events in space-time). But the length of a 4-vector is invariant under Lorentz transformation, so it also doesn't Lorentz contract. So there is no conflict between special relativity and a constant Planck length.
41 comments
[ 1.7 ms ] story [ 103 ms ] threadIt's more accurate to talk about Planck scale and not think it as strict limit.
Planck scale is where the structure of spacetime itself becomes dominated by quantum effects and the structure of spacetime may start looking really strange. Strange theories like loop quantum gravity, causal sets, causal dynamical triangulation, fractal cosmology, etc. work at Planck scale. According to fractal cosmology spacetime is 2-dimensional in Planck scale and gradually becomes 4-dimensional in larger scales. Loop quantum gravity sees it as "foamy".
Planck scale is also the area where measuring distances (differentiating with different positions in space) becomes impossible.
Which suggests internal structure of some kind.
I'm wary of any explanation that says "Well, it's just random", because randomness turns out to be a complicated process.
It's hard to imagine that some kind of prototypical base quantum would be inherently random just because.
I suppose it's possible. But it would be unexpected.
These units are very useful in QM and as "constants" (not the best choice of words since Planck units intentionally ignore constant values to some extent) that can be used to describe a relativistic universe.
*You can use Planck Length/Time to put a lower limit on any possible wavelength that below it a wave cannot exist, other Planck units can also be in the ballpark of the smallest possible unit/quanta of various things in various theories.
The uncertainty principle states that the product of the standard deviation of the momentum and posisition of a particle is bounded from below by h/4pi, where h is the plank constant.
This means that, in order to probe small distances, we must have great uncertainty in the momentum invovled, which means that there must be a lot of kinetic energy in the system. As the distances we probe become smaller, we have an increasing amount of energy in a decreasing amount of space.
E=mc^2 tells us that energy and mass are interchangeable. Specifically, energy, like mass, causes gravity. In order to probe below the plank length, we would need to put so much gravity in so small a space that we would form a black hole. However, because we cannot observe the inside of a blackhole, this prevents us from observing anything smaller than the plank length.
The arbitrary constant is 1. How is 1 less arbitrary than 2, 42, or 3.14?
I don't get it - is it trying to say objects of Planck length wouldn't contract due to relativity? If so - why?
A different factor, like 2, is more arbitrary, since "* 2" can't be left out without changing the value.
You can make the claim that a "* 1" factor is lurking in there, but even from that perspective it's less arbitrary than "* 2", since we could claim that "* 2" also has a "* 1" lurking in it, and so on :)
However seeing the quantum effects like a version of compression, dark matter and dark energy which could be an ugly hack to stabilize matter and galaxies, the fractal self similarity of the universe is just too amusing to ignore :)
I feel like the whole "wave-particle duality" is already a hint that the true nature of reality may always remain outside of our observation capability.
In fact, I think that humans may be a little too biased towards picturing everything as made up of discrete parts ("particles"), and that is probably a byproduct of having visual eyesight. Can't wait to meet alien intelligences with completely different senses and see what they think. :)
Wave-particle duality is a bit of a misnomer it's more of a pop-sci concept, all particles are defined by their wave function and there isn't a "particle function".
And if you think that we are too biased towards picturing everything made out of discrete parts then you won't like QM which is basically what the Q stands for which is "quanta" as in the smallest clump-thing-w/e of something.
That said most people that choose to study physics in high school (year 10-12) and or college would be exposed to Quantum Field Theory which makes everything make considerably more sense when you start thinking about everything in terms of fields.
Once you no longer think of an electron as an individual thing but as a electron field that extends through all space and the particles are the quanta of that field as in localized excitations of the field which when they reach a certain amplitude or energy level bring forth something we can measure and identify as an electron.
I wish QFT would be popularized more because it would bring so many important concepts into the common sense realm and it would actually be easier to explain things like why do particle accelerators work.
If I have understood the article correctly one would be able to measure the length of a spaceship relative to the Planck length and deduce velocity, entirely locally (i.e. onboard the spaceship).
This is a fundamental departure from general relativity which says there is no special frame of reference.
There are many attempts to combine these theories into a universal theory (pun intended), but it is hard to check the corner cases where those theories differ. That's one of the reasons we build better and better particle accelerators.
Either way, it doesn't make sense to apply (pure) general relativity to the small scale, nor to apply (pure) quantum theory to the large scale. The physicists know for decades about of that issue and are already taking care of that.
For the most part particle accelerators are not needed to explain quantum gravity, we do use them to find "new physics" but this new physics is more in the lines of the known unknowns.
We also do apply relativity to small scales every day, without relativity muons could not be discovered and without relativity to some extent even large particle accelerators would not "work" because the effects of spatial contractions are pretty important for how we predict and analyse the data coming from particle accelerators especially the "messy kind" like the LHC.
As for the large scale stuff as mentioned earlier quantum gravity is pretty compatible with general relativity in terms of explaining how the universe that we see today looks and works, you can easily explain why and how the moon rotates around the earth, it does rely on a massless spin-2 particle called a graviton which is yet to be "discovered" and it does break if the graviton would have a different spin (for example spin-0 graviton).
So I don't really understand the notion of why people still think that quantum gravity and general relativity aren't compatible to the extent of "what the fuck is going on", which is odd since afterall GR isn't 100% compatible with the Standard Model either, since GR is background independent and does not care about the particular state or shape of space-time while SM does.
Not sure at which point you disagree with my statement, though.
Each theory is useful for various things because each theory provides you with certain tools and perspectives that are useful for performing specific tasks.
At the end every theory is a set of laws and abstractions you use theories to change the perspective of how you look at things but these are often abstracts.
You can look at particles as particles, waves or fields it doesn't change reality but every one of these viewpoints comes with its unique benefits and you can chose between them depending on what benefits you most to for a specific task or a situation.
Units don't match - ct^2 is in m*s, not m^2.
However this is wrong. The Planck length is the minimal length of a 4-vector (a 4-dimensional vector measuring the distance between two events in space-time). But the length of a 4-vector is invariant under Lorentz transformation, so it also doesn't Lorentz contract. So there is no conflict between special relativity and a constant Planck length.