Time component in physics

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• Delta2
In summary: This is why in relativity the time component is called the "time signature".https://en.m.wikipedia.org/wiki/Time_signatureIn relativity everything stems from the metric. In an inertial frame (and in units where c=1) the metric can be written ##ds^2=-dt^2+dx^2+dy^2+dz^2##. As you can see, there are three terms with a + sign and one term with a - sign, so this metric has a (-+++) signature. The only thing that distinguishes time from space is that there is only one time component and the signature is opposite. This is why in relativity the time component is called the "time signature

Delta2

Gold Member
Are there any theories in physics that allow for a time component of the various vector quantities besides the x,y,z components? For example the velocity of a particle to have a time component ##v_t## besides the x,y,z components ##v_x,v_y,v_z##

Dale said:
Yes, this is common in relativity. They are called four-vectors. For example, energy and momentum together form a four-vector where energy is the time component.

https://en.m.wikipedia.org/wiki/Four-vector

I knew about this but this is not quite what I was thinking.. For example we put the energy together with the momentum as a 4-vector for reasons that suit our computations and equations to be expressed in a compact and elegant form. I mean i just view Energy as just the 4th component of the energy-momentum 4-vector. OR is there some deep conceptual reason that you called the energy the time component of the energy momentum vector?

I expected the time component to be defined in some sort of very special way...

Delta² said:
I mean i just view Energy as just the 4th component of the energy-momentum 4-vector.
I don’t see the difference with this and what you said previously

Delta² said:
I expected the time component to be defined in some sort of very special way...
The time component is just the one with the opposite sign in the signature.

Delta² said:
I knew about this but this is not quite what I was thinking.. For example we put the energy together with the momentum as a 4-vector for reasons that suit our computations and equations to be expressed in a compact and elegant form. I mean i just view Energy as just the 4th component of the energy-momentum 4-vector. OR is there some deep conceptual reason that you called the energy the time component of the energy momentum vector?

You can't transform 3-momentum between frames. To put it crudely, the "energy" in one frame is made up of some of the energy and some of the momentum, as measured in another frame. That's pretty deep.

Dale said:
The time component is just the one with the opposite sign in the signature.
Huh? Excuse me I don't understand. I guess deep special humour hehe?
PeroK said:
You can't transform 3-momentum between frames. To put it crudely, the "energy" in one frame is made up of some of the energy and some of the momentum, as measured in another frame. That's pretty deep.

Ok fine, that's an interesting property, the ability to transform 4-momentum between different frames. I was expecting that you would tell me that conservation of the 3-momentum relates to the translational spatial symmetry, while conservation of energy relates to time symmetry, that's another deep reason I can think of.

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Delta² said:
I was expecting that you would tell me that conservation of the 3-momentum relates to the translational spatial symmetry, while conservation of energy relates to time symmetry, that's another deep reason I can think of
Yes, that is true too.

Delta² said:
Huh? Excuse me I don't understand. I guess deep special humour hehe?
Sorry, I mistakenly assumed since you knew about four-vectors you also knew about signatures. I am not sure now what you know and what you don’t, so please forgive me if I under or over explain.

In relativity everything stems from the metric. In an inertial frame (and in units where c=1) the metric can be written ##ds^2=-dt^2+dx^2+dy^2+dz^2##. As you can see, there are three terms with a + sign and one term with a - sign, so this metric has a (-+++) signature. The only thing that distinguishes time from space is that there is only one time component and the signature is opposite.

Delta2

1. What is the concept of time in physics?

The concept of time in physics refers to the measurement of the duration of events and the ordering of these events. It is often described as the fourth dimension in the universe and is essential in understanding the behavior and interactions of physical objects.

2. Can time be measured and quantified?

Yes, time can be measured and quantified using a variety of units such as seconds, minutes, hours, and years. In physics, time is typically measured using a clock or a stopwatch that counts the number of oscillations in a standard unit of time, such as the vibration of a quartz crystal.

3. Is time constant or can it vary?

According to Einstein's theory of relativity, time is not constant and can vary depending on the speed and gravitational forces of an observer. This phenomenon is known as time dilation and has been experimentally proven through the use of atomic clocks.

4. How does time relate to space in physics?

In physics, time and space are intertwined and are often referred to as the space-time continuum. This means that time and space are not independent of each other but are rather interconnected and can affect each other's properties.

5. What is the arrow of time and how does it relate to the second law of thermodynamics?

The arrow of time refers to the one-way direction of time, from the past to the future. This is often associated with the second law of thermodynamics which states that the entropy, or disorder, of a closed system will always increase over time, giving a sense of direction to time's flow.