4 ms·

A consequence of time is that every event does not all happen at once. A consequence of space is that everything is not all in one place. Perhaps a consequence

A consequence of time is that every event does not all happen at once. A consequence of space is that everything is not all in one place. Perhaps a consequence of spacetime is that events have a location and a moment, but no guarantee of order?

hndamien 8y ago
I've always been confused that due to time dilation, everything from the perspective of a photon happens all at once, yet there is an order. If time is effectively dilated to the point that time has stopped for the photon, what happens in the year of travel over a light year of distance?
- gotocake 8y ago
  It can’t be stated enough: photons don’t have a perspective. Talking about what a photon “sees” is a non-starter. It’s also important to note that light follows null geodesics in spacetime, and while on paper that can look like no time elapses between emission and absorption, it still can’t tell us what it would “be like” to be a photon. If you want to go in that direction though, then this could help. As you approach c, length contraction in the direction of travel is extreme. In “theory” a photon doesn’t really travel at all, the universe is flattened like a pancake in the direction of its travel. There is no time for events to occur “at once” and no year passes on a lightlike curve. A photon is emitted and absorbed without a “subjective” interval, so talking about what such an interval might be missing that point.
  - raattgift 8y ago
    > Talking about what a photon "sees" is a non-starter In QED or other photon-containing QFTs like the Standard Model, it is not only a "starter", it is essentially the point of the thing. Surely the photon "sees" the electron in a Compton scattering? Photons obey the spin statistics for massless gauge bosons, so they can pile up at one point in spacetime. Equivalently, null geodesics can intersect. There can be a spacetime-point occupied by a pair of photons while the rest of spacetime is filled with points where they are occupied by only one (or neither). (Indeed, the Penrose theorem arises because null geodesics, and photons travelling on them, can collide and stay collided, so for this and other reasons there may be multiple points in spacetime occupied by both of our pair of photons.) One must be able to understand that for a photon there may be an early/late distinction -- either it is in a gravitational singularity or it isn't; either it is occupying a point with the other of our pair of photons or it isn't; either it's scattering or isn't. Following the photon and thinking about what it experiences, we can't use proper time, since it will be identical (practically[1]) everywhere along its path; likewise, spacetime intervals for all photons travelling on null geodesics are zero. The need for this understanding increases with photon interactions with charged matter: a pair of photons from different quasars arriving at a pair of detectors here tells us something about the location in spacetime of the quasar and about the metric expansion of space. Using cosmological coordinates, for each of the pair there is a _time_ before which no point in space contains it, and a time when they arrive at a detector on or around Earth. Given that each of the pair is from a different quasar, generally the emission time will be different. Moreover, at emission the wavelength of the photon will be shorter, and it will be longer at later times, right up to detection. Proper time (and proper length for wavelength) makes a mess of this in general, but we do not need to parameterize a non-timelike geodesic with proper time. Instead, for a null geodeseic, we use an affine parameter and consider its properties at each value of the affine parameter. For each of our quasar photons, at different affine parameter values the photon has a different energy-momentum. For the Minkowski vacuum photons in the first paragraph above, for a given affine parameter value, one photon is in vacuum or it is at the same point as the other photon. For accuracy, when we are dealing with physical photons, the stress-energy-momentum tensor must encode this. As we get away from simple Minkowski vacuum, we want all the tensor-fields to be accurate. We can recast your second paragraph's second sentence as taking the limit of the geodesic in which it becomes null, parameterizing by an un-rescaled extremized proper time. We can simply rescale so that we always have a different value at each point on the geodesic as we take this limit. Indeed, we can substitute any monotonic function of spacetime position on the geodesic and get a way to compare field-properties. For a timelike geodesic, proper time tends to be a "good" choice. The affine parameter, the unique monotonic function that satisfies the geodesic equation, tends to be a "good" choice for a null geodesic, in particular because it preserves the tangent vectors under parallel transport. - -- [1] Photons generally do not move at c in a medium, and one can describe this in a variety of equivalent ways, some of which demote a photon from a null curve to a timelike one while interacting with the bulk of the medium. There are serious proposals to study laboratory ultra-slow light in the context of General Relativity. From a theoretical perspective, Gordon in 1923 outlined an https://en.wikipedia.org/wiki/Optical_metric https://en.wikipedia.org/wiki/Optical_metric in which light follows different geodesics from the null geodesics sourced by the metric tensor, and there are various approaches to extending this to media with nonnegligible dispersion. In this sort of approach, a photon or a pulse of classical light can have a pretty conventional proper time.
    - gotocake 8y ago
      You are a really good teacher, thank you!
gotocake 8y ago
There is a guarantee of the order of causally related events, just not an absolute timing. All observers will agree that Alice throws a ball which Bill later catches, but different observers will disagree on when these events occurred exactly. They will however all agree that the order is Alice throws, Bill catches, and none will see Bill catch a ball that Alice later throws. To use the lightning bolt example from Einstein, different observers will disagree on the timing of the strikes, and whether or not they’re simultaneous. If one of the bolts strikes Alice and she goes flying though, everyone will agree that the order of events insofar as Alice is struck before she’s launched. This all assumes no FTL or CTCs of course, with either you would lose causality and events separated by spacelike intervals could influence each other.
- pentops 8y ago
  > All observers will agree that Alice throws a ball which Bill later catches I think this needs qualification. If I am stood directly behind Alice or Bill then it is possible I never see the interaction at all even though I am an observer, just as if I hold a two identical pencils together and look at them from the correct angle I observe only a single pencil. The important thing is in all cases, observers "see" space-time interactions as the geodesic of the event projected on to their own observational frame. Through that projection it is possible to lose degrees of freedom which can be space-time etc. It's through this projection that HUP emerges since if in the observational frame the time dimension is limited, the projected time axis of the event tends toward zero.
_Microft 8y ago
Maybe this is a helpful link? https://en.wikipedia.org/wiki/Relativity_of_simultaneity https://en.wikipedia.org/wiki/Relativity_of_simultaneity
goldenkey 8y ago
Given a fixed maximum speed of action, the speed of light, events in spacetime can be ordered via metric = x^2 + y^2 + z^2 - ct^2 But yes, you are sort of correct, two events can have the same metric, and one would not be able to distinguish which of them is responsible, if they are both capable of becoming present at the same speed.
posterboy 8y ago
The traditional notion is, where one thing is, there cannot be another.

hndamien 8y ago

I've always been confused that due to time dilation, everything from the perspective of a photon happens all at once, yet there is an order. If time is effectively dilated to the point that time has stopped for the photon, what happens in the year of travel over a light year of distance?

gotocake 8y ago
It can’t be stated enough: photons don’t have a perspective. Talking about what a photon “sees” is a non-starter. It’s also important to note that light follows null geodesics in spacetime, and while on paper that can look like no time elapses between emission and absorption, it still can’t tell us what it would “be like” to be a photon. If you want to go in that direction though, then this could help. As you approach c, length contraction in the direction of travel is extreme. In “theory” a photon doesn’t really travel at all, the universe is flattened like a pancake in the direction of its travel. There is no time for events to occur “at once” and no year passes on a lightlike curve. A photon is emitted and absorbed without a “subjective” interval, so talking about what such an interval might be missing that point.
- raattgift 8y ago
  > Talking about what a photon "sees" is a non-starter In QED or other photon-containing QFTs like the Standard Model, it is not only a "starter", it is essentially the point of the thing. Surely the photon "sees" the electron in a Compton scattering? Photons obey the spin statistics for massless gauge bosons, so they can pile up at one point in spacetime. Equivalently, null geodesics can intersect. There can be a spacetime-point occupied by a pair of photons while the rest of spacetime is filled with points where they are occupied by only one (or neither). (Indeed, the Penrose theorem arises because null geodesics, and photons travelling on them, can collide and stay collided, so for this and other reasons there may be multiple points in spacetime occupied by both of our pair of photons.) One must be able to understand that for a photon there may be an early/late distinction -- either it is in a gravitational singularity or it isn't; either it is occupying a point with the other of our pair of photons or it isn't; either it's scattering or isn't. Following the photon and thinking about what it experiences, we can't use proper time, since it will be identical (practically[1]) everywhere along its path; likewise, spacetime intervals for all photons travelling on null geodesics are zero. The need for this understanding increases with photon interactions with charged matter: a pair of photons from different quasars arriving at a pair of detectors here tells us something about the location in spacetime of the quasar and about the metric expansion of space. Using cosmological coordinates, for each of the pair there is a _time_ before which no point in space contains it, and a time when they arrive at a detector on or around Earth. Given that each of the pair is from a different quasar, generally the emission time will be different. Moreover, at emission the wavelength of the photon will be shorter, and it will be longer at later times, right up to detection. Proper time (and proper length for wavelength) makes a mess of this in general, but we do not need to parameterize a non-timelike geodesic with proper time. Instead, for a null geodeseic, we use an affine parameter and consider its properties at each value of the affine parameter. For each of our quasar photons, at different affine parameter values the photon has a different energy-momentum. For the Minkowski vacuum photons in the first paragraph above, for a given affine parameter value, one photon is in vacuum or it is at the same point as the other photon. For accuracy, when we are dealing with physical photons, the stress-energy-momentum tensor must encode this. As we get away from simple Minkowski vacuum, we want all the tensor-fields to be accurate. We can recast your second paragraph's second sentence as taking the limit of the geodesic in which it becomes null, parameterizing by an un-rescaled extremized proper time. We can simply rescale so that we always have a different value at each point on the geodesic as we take this limit. Indeed, we can substitute any monotonic function of spacetime position on the geodesic and get a way to compare field-properties. For a timelike geodesic, proper time tends to be a "good" choice. The affine parameter, the unique monotonic function that satisfies the geodesic equation, tends to be a "good" choice for a null geodesic, in particular because it preserves the tangent vectors under parallel transport. - -- [1] Photons generally do not move at c in a medium, and one can describe this in a variety of equivalent ways, some of which demote a photon from a null curve to a timelike one while interacting with the bulk of the medium. There are serious proposals to study laboratory ultra-slow light in the context of General Relativity. From a theoretical perspective, Gordon in 1923 outlined an https://en.wikipedia.org/wiki/Optical_metric https://en.wikipedia.org/wiki/Optical_metric in which light follows different geodesics from the null geodesics sourced by the metric tensor, and there are various approaches to extending this to media with nonnegligible dispersion. In this sort of approach, a photon or a pulse of classical light can have a pretty conventional proper time.
  - gotocake 8y ago
    You are a really good teacher, thank you!

gotocake 8y ago

There is a guarantee of the order of causally related events, just not an absolute timing. All observers will agree that Alice throws a ball which Bill later catches, but different observers will disagree on when these events occurred exactly. They will however all agree that the order is Alice throws, Bill catches, and none will see Bill catch a ball that Alice later throws. To use the lightning bolt example from Einstein, different observers will disagree on the timing of the strikes, and whether or not they’re simultaneous. If one of the bolts strikes Alice and she goes flying though, everyone will agree that the order of events insofar as Alice is struck before she’s launched. This all assumes no FTL or CTCs of course, with either you would lose causality and events separated by spacelike intervals could influence each other.

pentops 8y ago
> All observers will agree that Alice throws a ball which Bill later catches I think this needs qualification. If I am stood directly behind Alice or Bill then it is possible I never see the interaction at all even though I am an observer, just as if I hold a two identical pencils together and look at them from the correct angle I observe only a single pencil. The important thing is in all cases, observers "see" space-time interactions as the geodesic of the event projected on to their own observational frame. Through that projection it is possible to lose degrees of freedom which can be space-time etc. It's through this projection that HUP emerges since if in the observational frame the time dimension is limited, the projected time axis of the event tends toward zero.

_Microft 8y ago

Maybe this is a helpful link? https://en.wikipedia.org/wiki/Relativity_of_simultaneity https://en.wikipedia.org/wiki/Relativity_of_simultaneity

goldenkey 8y ago

Given a fixed maximum speed of action, the speed of light, events in spacetime can be ordered via metric = x^2 + y^2 + z^2 - ct^2 But yes, you are sort of correct, two events can have the same metric, and one would not be able to distinguish which of them is responsible, if they are both capable of becoming present at the same speed.

posterboy 8y ago

The traditional notion is, where one thing is, there cannot be another.