6 ms·

The reason we know that neutrinos aren't massless is that they oscillate between neutrino types. A massless particle must always travel at c, so it doesn't expe

by not2b 5y ago

The reason we know that neutrinos aren't massless is that they oscillate between neutrino types. A massless particle must always travel at c, so it doesn't experience time, so it can't decay or change into another particle.

pdonis 5y ago
> A massless particle must always travel at c, so it doesn't experience time, so it can't decay or change into another particle. This is not correct, although it's a common pop science misconception. For example, photons are massless, but they can undergo interactions that, for example, produce particle-antiparticle pairs. If your statement here were true, photons would be unable to undergo any interaction at all. A correct statement would be, heuristically, that if all three neutrino flavors were massless, they would all have the same mass, namely zero, so they would all oscillate exactly the same way, so any neutrino state that started out as one particular mixture of flavors would stay the same mixture forever. For example, neutrinos that were produced in an interaction like those in the Sun, which only produces electron neutrinos, would stay electron neutrinos forever. But this would also be true if the different neutrino flavors all had nonzero mass, but all the same nonzero mass. The only way for the mixture of neutrino flavors to change as the neutrinos travel is for the different flavors to have different masses. One of those masses could in principle be zero, but only one, not all three.
- 6nf 5y ago
  > photons are massless, but they can undergo interactions Not by themselves. They have to bump into other particles to interact. Photons in motion do not experience time and can not 'change flavour' or whatever without bumping into something else. Photon decay is not an observed phenomenon and can only happen if a photon has a non zero mass.
  - pdonis 5y ago
    > Not by themselves. They have to bump into other particles to interact. Not necessarily. There is a very small, but nonzero, probability for photon scattering (due, heuristically, to the small but nonzero probability for photons to become virtual electron-positron pairs). The probability is small, but it is nonzero, and that is sufficient to invalidate your claim. > Photons in motion do not experience time This is not correct. A correct statement would be that the concept of "proper time" does not apply to massless objects (objects that move on null worldlines) at all (it's mathematically ill-defined). But that does not mean there are not distinct events on a photon's worldline and that things cannot happen at those events even if the photon is moving by itself.
    - 6nf 5y ago
      Can you link me to a source stating that photons moving at C does or does not experience time? I'm not a layman, give it to me straight. I'm happy to work through the math or whatever is needed. I'm asking because I'm very sure that you are wrong here and I would like to be convinced otherwise if possible. The Minkowski metric ensures that photons moving at C can not experience local time.
      - pdonis 5y ago
        > I'm very sure that you are wrong here What actual textbooks on relativity have you studied? If you haven't studied any, I would strongly suggest doing so before being this confident about your beliefs about relativity. Many pop science sources (including, unfortunately, books by physicists who should know better but who can't help themselves when there are no other experts peer reviewing their work) will say the kinds of things you're saying about photons "not experiencing time", but you won't find a textbook or peer-reviewed paper that says them, because such misstatements are weeded out. Sean Carroll has a set of free online lecture notes [1] that make a good start (they're more focused on GR than SR but they have an introductory section that covers SR). Taylor & Wheeler's Spacetime Physics [2] is a good introductory textbook as well. The fundamental physical point here is that timelike objects (objects with positive rest mass that follow timelike worldlines) and lightlike objects (objects with zero rest mass that follow null worldlines) are different things, and the concept of "experienced time" or "proper time" (the latter is the correct technical term) only applies to timelike objects. The mathematical basis for this is that timelike worldlines can be parameterized by arc length, and arc length along a timelike worldline corresponds to elapsed time on a clock following that worldline. Null worldlines, however, cannot be parameterized by arc length at all, so the fact that arc length along them is zero does not mean lightlike objects "experience no time", it means that the whole concept of "experienced time" doesn't even work for them: it's mathematically invalid since it requires parameterizing the worldline by arc length. Another way of seeing the fundamental difference is to look at how Lorentz transformations act on timelike and null vectors. Lorentz transformations hyperbolically rotate timelike vectors: that means the transformation changes which way in spacetime the vector points, without changing its length. But Lorentz transformations do not rotate null vectors: they dilate them, meaning they increase or decrease all components of the vector by the same factor, without changing its direction in spacetime. This means that a null vector is not a "limiting case" of any set of timelike vectors as far as the Lorentz transformations are concerned; null and timelike vectors are simply two disconnected sets of vectors with respect to Lorentz transformations. Which in turn means that the common pop science image of objects "experiencing less time" as they move faster and faster, until photons moving at the speed of light "experience no time" in the limit, is not correct: it is not a valid description of what is actually happening in the math. Lorentz transformations don't change the length of timelike vectors at all, so they don't change the "experienced time" along them. The apparent "time dilation" of an object that is moving relative to you is due to the angle in spacetime between your worldline and the object's worldline, not to any property of the object's worldline itself. But the "angle" here is a hyperbolic angle, and the hyperbolic angle between your worldline (you being a timelike object) and any null worldline (i.e., any worldline of a light ray or photon) is infinite--in other words, mathematically ill-defined. In short, pop science authors who make claims like "photons don't experience time" are putting an interpretation on the fact that a photon's worldline has zero length in the Minkowski metric that is not justified by anything in the actual math. They do it, unfortunately, because they believe (quite possibly correctly) that saying things like that, even if they're wrong, will sell more books than trying to teach their readers the actual science. [1] https://arxiv.org/abs/gr-qc/9712019 https://arxiv.org/abs/gr-qc/9712019 [2] https://www.eftaylor.com/spacetimephysics/ https://www.eftaylor.com/spacetimephysics/
- zeusk 5y ago
  Does polarization (or polarization based filtering) of a photon qualify as an interaction based on time?
  - pdonis 5y ago
    Polarization based filtering involves other objects besides the photon being present, so it is not quite the kind of thing we're discussing. We're discussing the possibility of a photon just by itself, with nothing else present, undergoing some kind of change. There is a small probability of this happening; it's small, but it's not zero. So the claim that the photon's worldline being null (i.e., having zero "length" in terms of the metric of spacetime) prevents it from undergoing any change whatever as it travels is not true.
    - zeusk 5y ago
      Ah, does doppler effect or relativistic stretching affect the photon wave packet? I was told, that's what causes red/blue shift but aren't photons immune to relativistic effects since they travel at v = c?
      - pdonis 5y ago
        > does doppler effect or relativistic stretching affect the photon wave packet? Yes. > aren't photons immune to relativistic effects since they travel at v = c? No. Lorentz transformations still affect photons; they just affect them by dilation (they change all of the components of the photon's wave vector by the same factor, without changing the direction the wave vector points) rather than by hyperbolic rotation.
kmm 5y ago
Only two of the three neutrinos need to be massless, though that would be quite a curious asymmetry, and everyone expects all three to have mass. A massless particle might not have a restframe or experience proper time, but it still propagates through spacetime, and can definitely decay to other massless particles, at least in theory. After all, moving at the speed of light doesn't preclude it from interacting with ordinary matter either. "Luckily", in our universe there are theoretical reasons for photons to be completely stable (e.g. see https://arxiv.org/abs/hep-th/9508018 https://arxiv.org/abs/hep-th/9508018 ), but there's no such general rule.

by not2b 5y ago

pdonis 5y ago

> A massless particle must always travel at c, so it doesn't experience time, so it can't decay or change into another particle. This is not correct, although it's a common pop science misconception. For example, photons are massless, but they can undergo interactions that, for example, produce particle-antiparticle pairs. If your statement here were true, photons would be unable to undergo any interaction at all. A correct statement would be, heuristically, that if all three neutrino flavors were massless, they would all have the same mass, namely zero, so they would all oscillate exactly the same way, so any neutrino state that started out as one particular mixture of flavors would stay the same mixture forever. For example, neutrinos that were produced in an interaction like those in the Sun, which only produces electron neutrinos, would stay electron neutrinos forever. But this would also be true if the different neutrino flavors all had nonzero mass, but all the same nonzero mass. The only way for the mixture of neutrino flavors to change as the neutrinos travel is for the different flavors to have different masses. One of those masses could in principle be zero, but only one, not all three.

6nf 5y ago
> photons are massless, but they can undergo interactions Not by themselves. They have to bump into other particles to interact. Photons in motion do not experience time and can not 'change flavour' or whatever without bumping into something else. Photon decay is not an observed phenomenon and can only happen if a photon has a non zero mass.
- pdonis 5y ago
  > Not by themselves. They have to bump into other particles to interact. Not necessarily. There is a very small, but nonzero, probability for photon scattering (due, heuristically, to the small but nonzero probability for photons to become virtual electron-positron pairs). The probability is small, but it is nonzero, and that is sufficient to invalidate your claim. > Photons in motion do not experience time This is not correct. A correct statement would be that the concept of "proper time" does not apply to massless objects (objects that move on null worldlines) at all (it's mathematically ill-defined). But that does not mean there are not distinct events on a photon's worldline and that things cannot happen at those events even if the photon is moving by itself.
  - 6nf 5y ago
    Can you link me to a source stating that photons moving at C does or does not experience time? I'm not a layman, give it to me straight. I'm happy to work through the math or whatever is needed. I'm asking because I'm very sure that you are wrong here and I would like to be convinced otherwise if possible. The Minkowski metric ensures that photons moving at C can not experience local time.
    - pdonis 5y ago
      > I'm very sure that you are wrong here What actual textbooks on relativity have you studied? If you haven't studied any, I would strongly suggest doing so before being this confident about your beliefs about relativity. Many pop science sources (including, unfortunately, books by physicists who should know better but who can't help themselves when there are no other experts peer reviewing their work) will say the kinds of things you're saying about photons "not experiencing time", but you won't find a textbook or peer-reviewed paper that says them, because such misstatements are weeded out. Sean Carroll has a set of free online lecture notes [1] that make a good start (they're more focused on GR than SR but they have an introductory section that covers SR). Taylor & Wheeler's Spacetime Physics [2] is a good introductory textbook as well. The fundamental physical point here is that timelike objects (objects with positive rest mass that follow timelike worldlines) and lightlike objects (objects with zero rest mass that follow null worldlines) are different things, and the concept of "experienced time" or "proper time" (the latter is the correct technical term) only applies to timelike objects. The mathematical basis for this is that timelike worldlines can be parameterized by arc length, and arc length along a timelike worldline corresponds to elapsed time on a clock following that worldline. Null worldlines, however, cannot be parameterized by arc length at all, so the fact that arc length along them is zero does not mean lightlike objects "experience no time", it means that the whole concept of "experienced time" doesn't even work for them: it's mathematically invalid since it requires parameterizing the worldline by arc length. Another way of seeing the fundamental difference is to look at how Lorentz transformations act on timelike and null vectors. Lorentz transformations hyperbolically rotate timelike vectors: that means the transformation changes which way in spacetime the vector points, without changing its length. But Lorentz transformations do not rotate null vectors: they dilate them, meaning they increase or decrease all components of the vector by the same factor, without changing its direction in spacetime. This means that a null vector is not a "limiting case" of any set of timelike vectors as far as the Lorentz transformations are concerned; null and timelike vectors are simply two disconnected sets of vectors with respect to Lorentz transformations. Which in turn means that the common pop science image of objects "experiencing less time" as they move faster and faster, until photons moving at the speed of light "experience no time" in the limit, is not correct: it is not a valid description of what is actually happening in the math. Lorentz transformations don't change the length of timelike vectors at all, so they don't change the "experienced time" along them. The apparent "time dilation" of an object that is moving relative to you is due to the angle in spacetime between your worldline and the object's worldline, not to any property of the object's worldline itself. But the "angle" here is a hyperbolic angle, and the hyperbolic angle between your worldline (you being a timelike object) and any null worldline (i.e., any worldline of a light ray or photon) is infinite--in other words, mathematically ill-defined. In short, pop science authors who make claims like "photons don't experience time" are putting an interpretation on the fact that a photon's worldline has zero length in the Minkowski metric that is not justified by anything in the actual math. They do it, unfortunately, because they believe (quite possibly correctly) that saying things like that, even if they're wrong, will sell more books than trying to teach their readers the actual science. [1] https://arxiv.org/abs/gr-qc/9712019 https://arxiv.org/abs/gr-qc/9712019 [2] https://www.eftaylor.com/spacetimephysics/ https://www.eftaylor.com/spacetimephysics/
zeusk 5y ago
Does polarization (or polarization based filtering) of a photon qualify as an interaction based on time?
- pdonis 5y ago
  Polarization based filtering involves other objects besides the photon being present, so it is not quite the kind of thing we're discussing. We're discussing the possibility of a photon just by itself, with nothing else present, undergoing some kind of change. There is a small probability of this happening; it's small, but it's not zero. So the claim that the photon's worldline being null (i.e., having zero "length" in terms of the metric of spacetime) prevents it from undergoing any change whatever as it travels is not true.
  - zeusk 5y ago
    Ah, does doppler effect or relativistic stretching affect the photon wave packet? I was told, that's what causes red/blue shift but aren't photons immune to relativistic effects since they travel at v = c?
    - pdonis 5y ago
      > does doppler effect or relativistic stretching affect the photon wave packet? Yes. > aren't photons immune to relativistic effects since they travel at v = c? No. Lorentz transformations still affect photons; they just affect them by dilation (they change all of the components of the photon's wave vector by the same factor, without changing the direction the wave vector points) rather than by hyperbolic rotation.

kmm 5y ago

Only two of the three neutrinos need to be massless, though that would be quite a curious asymmetry, and everyone expects all three to have mass. A massless particle might not have a restframe or experience proper time, but it still propagates through spacetime, and can definitely decay to other massless particles, at least in theory. After all, moving at the speed of light doesn't preclude it from interacting with ordinary matter either. "Luckily", in our universe there are theoretical reasons for photons to be completely stable (e.g. see https://arxiv.org/abs/hep-th/9508018 https://arxiv.org/abs/hep-th/9508018 ), but there's no such general rule.