This definition/description does not seem to require causality? — guptanishank

Causality is what distinguishes the temporal dimension from the other ones.

The problem with that specific definition is that time is not defined for light. Light has no frame of reference, and hence no time or space associated with it.

I see it as a fault with the model or the theory in relativity. A necessity when we apply quantitative stuff to qualitative concepts.

The problem with that specific definition is that time is not defined for light. Light has no frame of reference, and hence no time or space associated with it. — guptanishank

Exactly so. Light has no frame, travels in no specific direction, cannot rest, has no mass and exists in no time of its own. But all these things are defined by arbitrary selection of frame.
Light doesn't exist inside or outside a causal cone, but rather occupies the dimensionless singularity where the rotation of one type of dimension becomes the other type. Quite consistent with the mathematics of it all.

But all these things are defined by arbitrary selection of frame.
Light doesn't exist inside or outside a causal cone, but rather occupies the dimensionless singularity where the rotation of one type of dimension becomes the other type. — noAxioms

Could you explain all of this in a little more detail. I would love to get to the bottom of this. Thanks.

I know the model is mathematically consistent. The interpretation is after all, built on top of the math.
That's not the point I was trying to make. Time CANNOT be defined for all the objects this way, because of mathematical restrictions. It would be counter intuitive to say the least, that a now is not defined for every object as well. So every theory, built upon this concept of time, will not have a now for every object, because time itself was not defined for those objects, and we are trying to build a theory of now from the current concept of time.

Could you explain all of this in a little more detail. I would love to get to the bottom of this. Thanks.

I know the model is mathematically consistent. The interpretation is after all, built on top of the math.
That's not the point I was trying to make. Time CANNOT be defined for all the objects this way, because of mathematical restrictions. It would be counter intuitive to say the least, that a now is not defined for every object as well. — guptanishank

Not sure what all else to explain. A photon, or anything else with no rest-mass, is missing half the properties of a classic object due to the inability to be at rest in any frame.

So every theory, built upon this concept of time, will not have a now for every object, because time itself was not defined for those objects, and we are trying to build a theory of now from the current concept of time.

This part confused me since no object has a 'now'. Events do, and 'now' is only a self-reference to that event. Pair an event with any other event and the two events can be said to have pure spatial separation (temporally simultaneous) or pure temporal separation (spatially the same place) by aligning one of the axes to go through both events. If you don't think axes can be arbitrarily assigned, I ask where any of them are? Which direction is the X axis of the universe? There isn't one. There isn't a temporal one either. Choosing one is arbitrary, as per the principle of relativity, which is older than Galileo's work, even if the implications of that principle weren't worked out until a century ago.

No I did not mean to imply that axes can or cannot be arbitrarily assigned.
Every object has a separate now attached to it as a property.

That is why I said that time is a dimension, a fourth dimension to be precise, and I say that because there is in some sense a capacity - perhaps ontologically - to locate a what or that we are capable of describing it. We are within it, our frame of reference. — TimeLine

How is a dimension a locatable thing? It is purely conceptual. Think of the three spatial dimensions. How would you locate one of those dimensions around you? Any assigning of a dimension to the space around you would be a purely arbitrary act, not representing anything which actually exists there.

Every object has a separate now attached to it as a property. — guptanishank

OK, we're taking completely different things then. Ignore what I've said.