How many sorts of time are there in physics?

[pervect]

Some recent threads inspired me to want to make a list of the different notions of time we need in physics (As I write this, I am focussed on pecial and general relativity, but I've added some important notions that are used by other fields). Here's what I've come up with so far, I am interested if there are any additions or corrections.

• Proper time. This is the sort of time measured by a clock. Proper time is an interval between two events, but in special and general relativity, this interval, as mesured by a clock, depends on the path the clock takes. This dependency is sometimes referred to as the "twin paradox", though it's not inherently paradoxical.
• Coordinate time. The basic purpose of coordinate time is to assign a unique label (generally, a real number) to the time at which an event occurs. While we usually assign time coordinates based on the reading one or more clocks, proper time alone is not sufficient to define coordinate time as proper time alone has no notion of how to synchronize clocks.
• Causal time. Some events can be ordered by cause and effect. In special relativity, "light cones" are used to define the causal ordering. Given a primary and secondary event, the causal ordering is only defined when the secondary event is within the "light cone" of the primary event, either the past light cone or the future light cone.
• Thermodynamic time. This is sometimes called "the arrow of time". The laws of physics are, as far as we know, time symmetric and reversible. But many events in the real world are not reversible.
• Cosmological time. This is a specific type of coordinate time in general realtivity, but I believe it is important enough to get a brief mention and a place on the list.
• Experiential time. Perhaps there is a better name for this, it relates to the idea of how we experience time as human beings. It's more philosophical than the other notions of time on the list, and less tied to numbers and experiment. But I think it should be on the list.

That's pretty much all I had on my list. There might be some additions needed added if we wanted to discuss time in quantum mechanics, but I don't have much insight on the topic or what might need to be added.

 

[anuttarasammyak]

Thank you for a nice list. Looking at this list, I realized that thermodynamic time may be the only one that cannot be defined quantitatively. For example, is it possible to define one second of thermodynamic time?

 

[Filip Larsen]

Not sure if it fits in your list or would be considered one of already mentioned classes, but in celestial mechanics different forms of dynamical time has historically been used a lot.

 

[Jaime Rudas]

• Proper time. This is the sort of time measured by a clock. Proper time is an interval between two events, but in special and general relativity, this interval, as mesured by a clock, depends on the path the clock takes. This dependency is sometimes referred to as the "twin paradox", though it's not inherently paradoxical.
• Coordinate time. The basic purpose of coordinate time is to assign a unique label (generally, a real number) to the time at which an event occurs. While we usually assign time coordinates based on the reading one or more clocks, proper time alone is not sufficient to define coordinate time as proper time alone has no notion of how to synchronize clocks.
• [...]
• Cosmological time. This is a specific type of coordinate time in general realtivity, but I believe it is important enough to get a brief mention and a place on the list.

Are coordinate time and cosmological time the proper time of a given clock?

 

[Dale]

Are coordinate time and cosmological time the proper time of a given clock?

No. Proper time does not have a notion of simultaneity like coordinate time does.

 

[pines-demon]

Thank you for a nice list. Looking at this list, I realized that thermodynamic time may be the only one that cannot be defined quantitatively. For example, is it possible to define one second of thermodynamic time?

It is just the arrow of time, never heard of thermodynamics time.

 

[Jaime Rudas]

No. Proper time does not have a notion of simultaneity like coordinate time does.

Understood, but let me rephrase the question slightly: Is coordinate time equivalent to the proper time of a given clock?

 

[Nugatory]

Understood, but let me rephrase the question slightly: Is coordinate time equivalent to the proper time of a given clock?

In general, no. We can choose any coordinate system we please according to whatever amuses us, and there's no reason that the coordinates we choose have to match the readings of any clock anywhere (for a trivial example, consider the coordinates found by applying the transformation $t'=\ln t$ in flat spacetime where $t$ is an ordinary Minkowski time coordinate). It's hard to imagine why we might want to do that, but we can.

In practice, we often choose coordinates that correspond to proper time along the worldline of some clock, like say a clock that is at rest relative to us and our lab equipment, because it it's convenient. There are exceptions though: for example the Schwarzschild time coordinate is what a physically unrealizable clock an infinite distance from the gravitating body would read.

 

[Ibix]

Are coordinate time and cosmological time the proper time of a given clock?

I'd say that the proper time of a clock is only defined along its wordline, whereas coordinate and cosmological times are defined over a 4d region. So coordinate time can't be the same as the proper time of a clock. It can be the same as the proper time of a family of appropriately zeroed clocks (e.g. cosmological time being the time coordinate of the usual FLRW coordinates), but it does not have to be (e.g. FLRW in conformal coordinates, or Schwarzschild coordinates).

 

[Dale]

I'd say that the proper time of a clock is only defined along its wordline, whereas coordinate and cosmological times are defined over a 4d region.

This is also what I would say is the key difference. They have different domains. It can be that on the worldline of a given clock they have the same value, but even in that case they are defined over different domains.

 

[Jaime Rudas]

In general, no. We can choose any coordinate system we please according to whatever amuses us, and there's no reason that the coordinates we choose have to match the readings of any clock anywhere (for a trivial example, consider the coordinates found by applying the transformation $t'=\ln t$ in flat spacetime where $t$ is an ordinary Minkowski time coordinate).

Would conformal time, as defined by Davis & Lineweaver in equation (29), be an example of this?

 

[Ibix]

Would conformal time, as defined by Davis & Lineweaver in equation (29), be an example of this?

Yes - it's a time-dependant rescaling of cosmological time. Co-moving clocks tick cosmological time, and only tick conformal time at the epoch when $a=1$.

 

[pervect]

Not sure if it fits in your list or would be considered one of already mentioned classes, but in celestial mechanics different forms of dynamical time has historically been used a lot.

That's a good comment, it might be worth mentioning a list of commonly used coordinate time standards besides cosmological time. The list I am coming up with is rather long, however, and might divert from the simple focus. Some of the key players here would be the IAU (International Astronomical Union), the BIPM (the international keeper of the SI system of units), and, to a lesser extent, the IERS, though their mission is more general.