4 ms·

I'd be curious to know why the Planck length wouldn't be reference frame independent, though... (which may be explained in your links, but it will take some tim

by qrendel 11y ago

I'd be curious to know why the Planck length wouldn't be reference frame independent, though... (which may be explained in your links, but it will take some time to go through them).

danbruc 11y ago
Planck length, mass, time and so on are built from the most fundamental physical constants - the speed of light, the Planck constant and the gravitational constant - all of which are independent of the reference frame. But I don't think that is actually important. It has more to do with units, i.e. the concrete value of the speed of light is determined by the way we defined the meter and the second and the same holds for the other constants. But that has no physical content, the value 299,792,458 m/s is a historical accident and we could as well have ended up with 42 foo/bar. So what physicist do is just set those constants to one and get rid of those arbitrary numbers by choosing appropriatei units, e.g. the speed of light becomes one lightyear per year. Because nothing moves faster than the speed you can then also go further and measure velocities with a unitless value as a fraction of the speed of light, i.e. a number between zero and one, as it it appears in the equations of special relativity. So if you throw those constants together in relatively simple expressions like hG/c³ you again get one as the numerical value and here for example something with units of area, the Planck area. But there is also no real physical content in the Planck units beyond that. Because the laws of physics usually contain all the constants and values in small powers and with small factor like a Pi here and one half there those units define scales of length, time and so on where the quantities are all about one, nothing is ten to the twenty or minus thirty. So at that scales the laws of physics may show interesting behavior like (1 - v²/c²) becoming zero as v approaches c but that are also more like heuristics than hard truths. So to make a long story short, Planck units are frame independent because they are built from constants and they are nice to think in because many things are of order one - a black hole of one Planck mass has probably a horizon of one Planck area or four Pi Planck areas or something small like that - but they are not that special.
- qrendel 11y ago
  But you seem to be claiming that spacetime is unlikely to be quantized because the Planck length or Planck time, i.e. the quanta of length in spacetime, would be contracted in different reference frames. Therefore Planck units of length/time wouldn't be frame invariant - they'd depend upon your inertial reference frame. So claiming Planck units are frame independent violates the idea that spacetime can't be quantized (at least for the reason you stated), since the quanta would experience relativistic contraction and dilation. The explanation seems to go against your original comment. Edit: I may have given the wrong impression - when I said "Planck units" I meant quanta of space, time, area, etc. Not "natural units" where all relevant physical constants are taken to equal one. It appears the term "Planck units" refers to one of multiple sets of natural units, of which I was not aware: https://en.wikipedia.org/wiki/Natural_units#Planck_units https://en.wikipedia.org/wiki/Natural_units#Planck_units
  - TheOtherHobbes 11y ago
    It depends if relativistic behaviour is emergent or fundamental. The whole point of the "spacetime is quantised" argument isn't just to suggest that spacetime comes in little lumps, but to investigate the possibility that the properties of spacetime - including curvature, relativistic effects, and all the weirdness in quantum theory - emerge from a common fundamental description. Planck-scale invariance is a red herring - or rather, it's a naive assumption that may not be accurate. There isn't really much useful theory or experimental evidence in Planck-scale physics. For an overview, see http://newt.phys.unsw.edu.au/einsteinlight/jw/module6_Planck.htm http://newt.phys.unsw.edu.au/einsteinlight/jw/module6_Planck...
yk 11y ago
Roughly because of Lorentz boost, aka length contraction. So if I take some distance, say 1m, and I look at it from relativistic speed it gets contracted. And if I do that from high enough speeds, it gets contracted below the Planck length, so a fundamental length constant would violate Lorentz symmetry. Some people tried to construct such a theory, but as far as I understand, they are going nowhere. See https://en.wikipedia.org/wiki/Doubly_special_relativity https://en.wikipedia.org/wiki/Doubly_special_relativity
- mlonkibjuyhv 11y ago
  How about if length contraction means that 1 meter is now fewer length quanta than before? I mean if spacetime is emergent why limit ourselves to an intuitive sense of what distance is.
  - yk 11y ago
    Well, if you have less length quanta then we could call them a unit of length, they would no longer be any kind of fundamental property. ( But actually the notion of a particle is a rather big problem of quantum field theory in curved backgrounds.)
  - qrendel 11y ago
    This is essentially what I was asking - why wouldn't all inertial frames determine the size of length quanta to be the same, but disagree on the number of them between two events in spacetime.
amai 11y ago
Somebody already asked that for you: https://physics.stackexchange.com/questions/4094/is-the-planck-length-lorentz-invariant https://physics.stackexchange.com/questions/4094/is-the-plan...
wyager 11y ago
We have no reason to believe that the Planck length actually has any physical significance. It is just a way to get something of a certain order of magnitude from physical constants. The quantization in quantum mechanics arises from constraints on the physical systems being studied. There are no constraints that would lead to length itself being quantized. You can get wavelength quantization for bound particles, but that's just for that particle, not for space in general.

by qrendel 11y ago

I'd be curious to know why the Planck length wouldn't be reference frame independent, though... (which may be explained in your links, but it will take some time to go through them).

danbruc 11y ago

Planck length, mass, time and so on are built from the most fundamental physical constants - the speed of light, the Planck constant and the gravitational constant - all of which are independent of the reference frame. But I don't think that is actually important. It has more to do with units, i.e. the concrete value of the speed of light is determined by the way we defined the meter and the second and the same holds for the other constants. But that has no physical content, the value 299,792,458 m/s is a historical accident and we could as well have ended up with 42 foo/bar. So what physicist do is just set those constants to one and get rid of those arbitrary numbers by choosing appropriatei units, e.g. the speed of light becomes one lightyear per year. Because nothing moves faster than the speed you can then also go further and measure velocities with a unitless value as a fraction of the speed of light, i.e. a number between zero and one, as it it appears in the equations of special relativity. So if you throw those constants together in relatively simple expressions like hG/c³ you again get one as the numerical value and here for example something with units of area, the Planck area. But there is also no real physical content in the Planck units beyond that. Because the laws of physics usually contain all the constants and values in small powers and with small factor like a Pi here and one half there those units define scales of length, time and so on where the quantities are all about one, nothing is ten to the twenty or minus thirty. So at that scales the laws of physics may show interesting behavior like (1 - v²/c²) becoming zero as v approaches c but that are also more like heuristics than hard truths. So to make a long story short, Planck units are frame independent because they are built from constants and they are nice to think in because many things are of order one - a black hole of one Planck mass has probably a horizon of one Planck area or four Pi Planck areas or something small like that - but they are not that special.

qrendel 11y ago
But you seem to be claiming that spacetime is unlikely to be quantized because the Planck length or Planck time, i.e. the quanta of length in spacetime, would be contracted in different reference frames. Therefore Planck units of length/time wouldn't be frame invariant - they'd depend upon your inertial reference frame. So claiming Planck units are frame independent violates the idea that spacetime can't be quantized (at least for the reason you stated), since the quanta would experience relativistic contraction and dilation. The explanation seems to go against your original comment. Edit: I may have given the wrong impression - when I said "Planck units" I meant quanta of space, time, area, etc. Not "natural units" where all relevant physical constants are taken to equal one. It appears the term "Planck units" refers to one of multiple sets of natural units, of which I was not aware: https://en.wikipedia.org/wiki/Natural_units#Planck_units https://en.wikipedia.org/wiki/Natural_units#Planck_units
- TheOtherHobbes 11y ago
  It depends if relativistic behaviour is emergent or fundamental. The whole point of the "spacetime is quantised" argument isn't just to suggest that spacetime comes in little lumps, but to investigate the possibility that the properties of spacetime - including curvature, relativistic effects, and all the weirdness in quantum theory - emerge from a common fundamental description. Planck-scale invariance is a red herring - or rather, it's a naive assumption that may not be accurate. There isn't really much useful theory or experimental evidence in Planck-scale physics. For an overview, see http://newt.phys.unsw.edu.au/einsteinlight/jw/module6_Planck.htm http://newt.phys.unsw.edu.au/einsteinlight/jw/module6_Planck...

yk 11y ago

Roughly because of Lorentz boost, aka length contraction. So if I take some distance, say 1m, and I look at it from relativistic speed it gets contracted. And if I do that from high enough speeds, it gets contracted below the Planck length, so a fundamental length constant would violate Lorentz symmetry. Some people tried to construct such a theory, but as far as I understand, they are going nowhere. See https://en.wikipedia.org/wiki/Doubly_special_relativity https://en.wikipedia.org/wiki/Doubly_special_relativity

mlonkibjuyhv 11y ago
How about if length contraction means that 1 meter is now fewer length quanta than before? I mean if spacetime is emergent why limit ourselves to an intuitive sense of what distance is.
- yk 11y ago
  Well, if you have less length quanta then we could call them a unit of length, they would no longer be any kind of fundamental property. ( But actually the notion of a particle is a rather big problem of quantum field theory in curved backgrounds.)
- qrendel 11y ago
  This is essentially what I was asking - why wouldn't all inertial frames determine the size of length quanta to be the same, but disagree on the number of them between two events in spacetime.

amai 11y ago

Somebody already asked that for you: https://physics.stackexchange.com/questions/4094/is-the-planck-length-lorentz-invariant https://physics.stackexchange.com/questions/4094/is-the-plan...

wyager 11y ago

We have no reason to believe that the Planck length actually has any physical significance. It is just a way to get something of a certain order of magnitude from physical constants. The quantization in quantum mechanics arises from constraints on the physical systems being studied. There are no constraints that would lead to length itself being quantized. You can get wavelength quantization for bound particles, but that's just for that particle, not for space in general.