# Moving through Space-Time

#### menergyam

One thing that I really never understood is why space-time is connected. I have not taken general relativity yet, so I don't know the mathematics yet, but I want to know the answer.

Why does an object have to move through space-time? Why can't an object move only through space or only through time? Are the mathematical equations that describe space-time just imply that they are connected? Is it proven with experimental evidence? Or is it proven with mathematical equations that space and time are connected? Or is space and time connected because of a real fundamental reason?

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#### tiny-tim

Homework Helper
Welcome to PF!

Hi menergyam! Welcome to PF!
Why can't an object move only through space or only through time?
An object can move only through time …

most of the objects you're looking at right now are doing exactly that

and if an object moved only through space (and not through time), then it would be moving infinitely fast

#### A.T.

Why does an object have to move through space-time? Why can't an object move only through space or only through time?
Objects at rest move only through time. And you can think of light as moving only trough space, as it doesn't experience any time passing:

Are the mathematical equations that describe space-time just imply that they are connected?
They are not "connected", as they are fully independent dimensions. Putting them into one diagram doesn't mean anything physically.

Is it proven with experimental evidence?
There is nothing to prove here. Spacetime is just a mathematical model used to describe experimental observation.

#### menergyam

Everyone's so awesome!!!!!

#### menergyam

Wait, How can you tell if something is at absolute rest? You can only tell if something is at rest relative to something else. There is no absolute frame of reference, thats what I learned in special relativity. Also, our solar system is revolving around our galaxy, and our galaxy is moving relative to other galaxies. Therefore, we can't tell if something is moving only through time itself. Also, light does not move infinitely fast, it moves at the speed of light. Therefore, I am still confused, and my question is still not answered. Why can't an object move only through time or only through space?

#### JesseM

There's no objective or absolute sense in which something can be moving "only through time", you can only talk about the amount of "movement through time" vs. "movement through space" relative to a particular (arbitrary) choice of reference frame.

#### jefswat

Re: Welcome to PF!

Hi menergyam! Welcome to PF!

An object can move only through time …

most of the objects you're looking at right now are doing exactly that

and if an object moved only through space (and not through time), then it would be moving infinitely fast
I thought I read that all objects are moving through spacetime at c. So an object could either move through space at c and time at 0, time at c and space at 0, or some combination of the two. Why do you say it has to move infinitely fast?

#### menergyam

I was replying to tiny-tim when I was saying an object can not move infinitely fast.

#### menergyam

There's no objective or absolute sense in which something can be moving "only through time", you can only talk about the amount of "movement through time" vs. "movement through space" relative to a particular (arbitrary) choice of reference frame.
When you say that I can only talk about the amount of movement through time vs. movement through space, do you mean that by saying otherwise is pointless? Because there is no absolute sense? Since no absolute sense exists then my question does not exist as well, am I interpreting your answer correctly?

#### JesseM

When you say that I can only talk about the amount of movement through time vs. movement through space,
You left out the key part of that sentence...you can only talk about those things relative to a particular choice of reference frame.
menergyam said:
do you mean that by saying otherwise is pointless?
What do you mean by "saying otherwise"? It is indeed meaningless to talk about the amount of movement through time or space without specifying the context of what reference frame you're using...there is no absolute, frame-independent truth about how much you're moving through time or space.

#### menergyam

Okay, to clear up what I mean. I am taking into consideration about the frame of reference this time.

For example, I use a laboratory room on earth as my reference frame. If an atom is cooled to a few millionths of a degree above 0 K in the laboratory, then can't we say that this atom is not moving? It would possess very little kinetic energy. Wouldn't this atom be moving only through time and very little distance through space? This atom would exist in the same location for as long as it is in its cooled state. If the atom actually reached 0K, (I think this is not possible) wouldn't this mean that it travels through absolutely 0 distance relative to the laboratory?

Now, what I really want to know is the opposite in the scenario I said above. Can this atom move a certain distance say 10^12 meters in absolutely 0 time relative to the laboratory? This would mean that it moved, infinitely fast because you would be dividing by 0 to calculate speed.

#### HMS

Now, what I really want to know is the opposite in the scenario I said above. Can this atom move a certain distance say 10^12 meters in absolutely 0 time relative to the laboratory? This would mean that it moved, infinitely fast because you would be dividing by 0 to calculate speed.

For the motion of the atom to be completely confined to space and none of it in time, it will have to move at the speed of light like a photon.

#### tiny-tim

Homework Helper
Hi menergyam!
Wait, How can you tell if something is at absolute rest? You can only tell if something is at rest relative to something else. There is no absolute frame of reference, thats what I learned in special relativity. … Therefore, I am still confused, and my question is still not answered. Why can't an object move only through time or only through space?
Ah … this shows that space and time are connected …

when I said that a stationary object moves only through time (and not through space), that only applies in one frame. In any other frame, it moves through both space and time.

The phrase "motion only through time in any frame" makes no sense, since space and time are connected.
I was replying to tiny-tim when I was saying an object can not move infinitely fast.
I didn't say it can … I said "if …"

#### Phrak

Re: Welcome to PF!

Hi menergyam! Welcome to PF!

An object can move only through time …

most of the objects you're looking at right now are doing exactly that

and if an object moved only through space (and not through time), then it would be moving infinitely fast
A contrare (in my best continental accent). Things don't move through time. Things only move in space.

#### tiny-tim

Homework Helper
contrariare

Au contraire (in my best continental spelling) …

it depends what you mean by "move"

#### Phrak

Re: contrariare

Au contraire (in my best continental spelling) …

it depends what you mean by "move"
What are you doing up so late? It's nearly 4am here. What's the world coming to?

To "move" means to change from one place in space to another.

Now enter the world of maps where we pretend we are outside of space and time, looking in. Time is mapped onto some sheet of paper or our imagination to a spatial extent. So for this we have a "map language" so we can talk about the map without making grammatical errors. This is fine as long as everyone knows we are talking about the map. We look at all of time, or some amount of it as if it's a spatial extent. This way it makes map-sense to say things like "the future is", instead of "the future will be". Objects are now lines in spacetime. But nothing moves on the map. It's just a line of mappish present tense.

#### JesseM

Okay, to clear up what I mean. I am taking into consideration about the frame of reference this time.

For example, I use a laboratory room on earth as my reference frame. If an atom is cooled to a few millionths of a degree above 0 K in the laboratory, then can't we say that this atom is not moving? It would possess very little kinetic energy. Wouldn't this atom be moving only through time and very little distance through space? This atom would exist in the same location for as long as it is in its cooled state. If the atom actually reached 0K, (I think this is not possible) wouldn't this mean that it travels through absolutely 0 distance relative to the laboratory?

Now, what I really want to know is the opposite in the scenario I said above. Can this atom move a certain distance say 10^12 meters in absolutely 0 time relative to the laboratory? This would mean that it moved, infinitely fast because you would be dividing by 0 to calculate speed.
When people talk about moving through spacetime at c, and how this is divided up into moving through space and moving through time, they are making use of a particular definition of "movement through spacetime" and "movement through time" which may not be totally intuitive (and in fact you won't typically see these terms defined in a relativity textbook, it's a mathematical trick which I've only seen a few authors like Brian Greene make use of--see my post #3 on this thread for a quote from one of Greene's books where he explains the math). Basically, the "rate of movement through time" in a particular frame is defined as c times the ratio of the object's proper time (clock time) to coordinate time in that frame...so, if an object's clock is slowed down by a factor of two, its "speed through time" is then defined as 0.5c. Since time dilation approaches infinity as you approach the speed of light, under this definition your "speed through time" would be zero at the speed of light, it would not require you to move infinitely fast.

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