# Can we define time as a field? [closed]

The main objective is, can we relate time in terms of a field, I know time differs in many properties from an usual field. But I always imagine time as an forward moving field and we all know it is affected by gravitational field, so can we relate time as a field?

• Time is that which the clocks show, so if you want to have a time field, then you have to place a clock in every point in space. Commented Jan 22 at 14:18
• For your information, time exists before the clocks and it not the property of clock it is the property of space.
– Ash
Commented Jan 22 at 14:22
• I am not sure the time and frequency divisions at NIST will agree with you on that completely. What spacetime provides is the causality that allows us to synchronize clocks, but it does not provide "time" itself. Commented Jan 22 at 14:26
• no we can't do that because it depends on the observable, not only from the point in the space Commented Jan 22 at 14:28
• Surely you can only define time in a given reference frame ? Since there is no preferred reference frame there is no preferred time co-ordinate. Commented Jan 22 at 15:21

A field is just a function that is defined at each event in spacetime. So we could define a field $$f(t,x,y,z)=t$$ This would be time as a field.

we always imagine time as if a forward moving field

Fields don’t move, and this field doesn’t even have waves.

Note: there are two primary concepts of time. Proper time is the physical time measured by a clock. Coordinate time is the mathematical time defined in some coordinate systems.

This field would represent coordinate time. As such it is coordinate dependent and therefore often considered to be non-physical. It doesn’t obey any important field equations, so yes it can be treated as a field in a formal sense, but doing so does not bring any benefit that I can see.

• Around a Schwarzschild blackhole, time would ticking a different rates according to distance from the gravitational source according to the observer at 'infinity' no? I think it would effectively be the same as the gravitational potential field offhand.
– KDP
Commented Jan 22 at 17:17
• @KDP for spacetimes that have a timelike Killing vector and for coordinates that respect that symmetry, yes
– Dale
Commented Jan 22 at 18:05
• I appreciate your answer, we can conclude that obviously there is no absolute time and to represent coordinate time system we have to be specific about the obeserver. For different observer there must be different expression for coordinate time.
– Ash
Commented Jan 22 at 18:22
• @Ash yes, and sometimes even just specifying the observer is insufficient. E.g. for non-inertial observers there is no single coordinate system accepted as representing their frame
– Dale
Commented Jan 22 at 18:39

A field is a quantity which typically depends on the location like --- giving a simple example --- a temperature distribution over a piece of metal, on one end of the metal the temperature is low and other end the temperature is high. So the temperature is a function of the location where it is measured:

$$T = T(x)$$

That would be a temperature field.

In particular the temperature distribution can be predicted by physical laws, i.e. there is a relationship between a temperature value at a certain position and the temperature value in its neighourhood.

Of course on top of that one could be interested in the temperature distribution in time and location, i.e.

$$T =T(t,x)$$

On the other hand time is just a parameter, nothing more. Time depends on the chosen reference system, but not on the location.

One can make consider slices of spacetime where the time is the same, these slices depend on the reference system. Different observers at different locations have their proper time they measure, but one would never consider this as a field. Simply since there is no relationship between the individual (proper) times and the location where it is measured, rather it depends on the reference systems of the different observers. In particular each observer can choose its own reference system, which means that such a data set would be rather arbitrary.

• @foolishmuse But the observations of time depend on the observer and how they are moving. So there is no single "time field". Commented Jan 22 at 15:32
• @foolishmuse But if there was a single time at each point in space then the twins in the twins "paradox" would be the same age when they met again. Commented Jan 22 at 16:18
• @foolishmuse SR is just a limiting case of GR. If your idea of a universal "time field" won't work in SR then it won't work in GR either. Commented Jan 22 at 17:48
• @gandalf61 The electric field and magnetic field are observer dependent, eg the magnetic field can completely disappear in some reference frames, so it follows a field does not have to be observer independent to qualify as a field.
– KDP
Commented Jan 22 at 18:46
• @KDP Well, yes, obviously we can define a field in any arbitrary way that we like. "Distance from my current location" is a field. But a field that is observer dependent is not a physically useful entity. Which is precisely why we combine the electric and magnetic fields into the electromagnetic tensor. Commented Jan 22 at 20:42