Exploring the Relationship Between Space and Time

[1MileCrash]

Does it make sense to say that anything and everything, travels at lightspeed at all times, but what varies is whether or not it is traveling through space, time, or both?

For example, at a complete motionless standstill, I am traveling through time at C, but not traveling through space at all. My total speed is C.

I drive my corvette at 180 MPH. I am now moving through space, but at an extremely low speed when compared with C; Therefore I am still traveling almost entirely through time and only a bit through space, there will be no noticeable time dilation between me in my corvette and a stationary observer, however there is still some. My total speed is C.

I board a rocketship going 6/7 C. I am traveling faster through space and less fast through time; time dilation. But my total speed is still C.

And, at lightspeed, I am traveling entirely through space and not at all through time. My total speed is C.

Essentially I'm thinking that our total speed is always C, and that it is divided between space and time.


Does this work mentally? Could I even say that when I am driving at 180 MPH, I am traveling through time at a speed of ( C - 180 MPH )?



Typing this made me think more...how we experience the differences between space and time is all relative to how we move through them. Maybe some hypothetical lifeform in a hypothetical universe could see our space as time and our time as space, moves through our "space" at tiny fractions below C, which is their time, and move around our "time" at very very low speeds, which is their space, and think that we are zipping around in no time at all while we think the same about them. Is there any difference between space and time at all? I need to go to bed.

Could something traveling near C through space almost experience space as time and time as space? "See" motion through time of other bodies as motion through space?


Seriously, opening the tylenol PM now.

 

[Mentz114]

Yes, it does. In relativistic mechanics velocity is a 4-vector, having a time component as well as three spatial components. In your own frame the vector is $( c,0,0,0)$, and when boosted by a velocity $\beta$ in x-direction this becomes $\gamma( c, \beta,0,0)$, which has the same norm (total speed) as the unboosted velocity. So the total speed is the same for all inertial frames.

See here for a full explanation

http://en.wikipedia.org/wiki/Four-velocity

 

[ghwellsjr]

To answer your three questions:
No.
No.
No.

No matter how much you have accelerated so that you are now traveling at any speed, you can consider yourself at rest with respect to c. You cannot experience length contraction or time dilation or any other effect.

Or to think about it another way, you can consider yourself to be traveling at any speed in any direction by simply considering a frame of reference that is traveling at that speed in the opposite direction.

Why do you want to confuse the speed of light which is distance divided by time with time?

 

[1MileCrash]

No matter how much you have accelerated so that you are now traveling at any speed, you can consider yourself at rest with respect to c. You cannot experience length contraction or time dilation or any other effect.

Trying to reach C is impossible because of time dilation and length contraction. If I am running close to the speed of light and I increase my speed by 50 mph from my reference, it might look something like 5 millimeters per month to the stationary observer. You can increase your speed as much as you want but due to time dilation and length contraction the speed increase just doesn't add, it's like trying to catch up to the horizon.

Yes, I don't experience time dilation or length contraction, nor mass increase or anything else, nothing ever "experiences" these phenomenon, but it is still there relative to another frame of reference.

When I drive my car at 60 miles per hour, time as well as motion differs from a stationary (in space) frame of reference. Not much, because I'm traveling at such a low speed relative to C, but it's there.

I'm not keeping speed exclusively in space here. When something travels faster through space it MUST travel slower through time. Thus it's not illogical to say that there is always a total net speed through spacetime.

Or to think about it another way, you can consider yourself to be traveling at any speed in any direction by simply considering a frame of reference that is traveling at that speed in the opposite direction.

I don't see what any of this has to do with anything.

 

[ghwellsjr]

Since I posted my first response to your first post, you added three more questions (which I didn't answer) and now you are talking about spacetime instead of "space, time, or both". Mentz answer to you was regarding spacetime which is not the same thing as space and time. Note that the norm or total speed that he was talking about is c in all reference frames for all speeds.

But that wasn't what you were asking about because you were wondering if when you are traveling at 180 MPH, you are traveling through time at a speed of (c - 180 MPH). When you are considering spacetime, you have to square, add or subtract and take the square root of everything to make it come out right. And you have to keep your units consistent. You can't just take a difference.

But to address your last three questions--yes, there is a big difference between time and space. Space has three components and time has only one. The four-vectors combine all four of these components into one amalgamation called spacetime and no lifeforms will ever be able to get the one time component interchanged into the three space components or vice versa.

And to address your wondering what my comment about considering yourself to be traveling at any speed by considering a different frame of reference is to point out that what is important in Special Relativity are those things that remain invariant when viewed from different frames of reference. Your concept of moving through space and time where you add the two to get c (which is not correct), can generate arbitrary values that are not invariant.

 

[1MileCrash]

Checked out the wiki article better and man, it's pretty much exactly what I was talking about.
"In other words, the norm or magnitude of the four-velocity is always exactly equal to the speed of light. Thus all objects can be thought of as moving through spacetime at the speed of light. This provides a way of understanding time-dilation: as an object like a rocket accelerates from our perspective, it moves faster through space, but slower through time in order to keep the four-velocity constant. Thus to an observer, a clock on the rocket moves slower, as do the clocks in any reference frame that is not comoving with them. Light itself provides a special case- all of its motion is through space, so it does not have any "left over" four-velocity to move through time. Therefore light, and anything else traveling at light speed, do not experience the "flow" of time."

Perhaps I didn't phrase it as eloquently or correct but this is what I was trying to say.

Since I posted my first response to your first post, you added three more questions (which I didn't answer) and now you are talking about spacetime instead of "space, time, or both". Mentz answer to you was regarding spacetime which is not the same thing as space and time. Note that the norm or total speed that he was talking about is c in all reference frames for all speeds.

Above quote from wiki article

But that wasn't what you were asking about because you were wondering if when you are traveling at 180 MPH, you are traveling through time at a speed of (c - 180 MPH). When you are considering spacetime, you have to square, add or subtract and take the square root of everything to make it come out right. And you have to keep your units consistent. You can't just take a difference.

Okay, I have no idea on the math yet. But it is correct to say that moving through space at a speed will cause you to travel "proportionally" slower through time?

But to address your last three questions--yes, there is a big difference between time and space. Space has three components and time has only one. The four-vectors combine all four of these components into one amalgamation called spacetime and no lifeforms will ever be able to get the one time component interchanged into the three space components or vice versa.

I see, thanks.

And to address your wondering what my comment about considering yourself to be traveling at any speed by considering a different frame of reference is to point out that what is important in Special Relativity are those things that remain invariant when viewed from different frames of reference. Your concept of moving through space and time where you add the two to get c (which is not correct), can generate arbitrary values that are not invariant.

Okay. I understand this, but from the wiki article quote, how do we define that the rocket is actually moving at all, what is it's motion supposed to be relative to? What you're getting at is the absense of a "master reference" essentially right?

 

[ghwellsjr]

Okay, I have no idea on the math yet. But it is correct to say that moving through space at a speed will cause you to travel "proportionally" slower through time?

No, you have to consider all four components of the four-vector when discussing the four-velocity and in all cases the norm (which is the invariant magnitude of the vector) is the speed of light. Think of a different kind of problem, that of defining your velocity on the surface of the ground. You could say that you are traveling 35 miles per hour north and 35 miles per hour east (because you are actually traveling 50 miles per hour north-east). But there is no meaning to the idea that the two components of 35 MPH add up to 70 MPH or have any real or actual significance. You could use a rotated co-ordinate system in which those two number were different, one being larger and the other being smaller. Your choice of co-ordinate system determines the particular values that you get but it is only the magnitude (50 MPH) that has any meaning or significance.

In the same way, you can consider the four-velocity in a relativity scenarion but the individual components cannot be taken separately, it is only the magnitude (the norm) which has any meaning or is significant and that is alway c.

Okay. I understand this, but from the wiki article quote, how do we define that the rocket is actually moving at all, what is it's motion supposed to be relative to? What you're getting at is the absense of a "master reference" essentially right?

We always define all motions (and positions and times) relative to a fixed arbitrarily defined frame of reference, pick anyone you want. You can treat it as a "master reference". But you have to do everything in that one frame. If we are talking about thought problems, then the problem itself defines a frame of reference and it is generally easiest to do the analysis in that same frame of reference rather than transform the whole scenario into another frame of reference, which can be exceedingly difficult to do. In fact, most if not all of the so-called paradoxes in SR are nothing more than mistakes made in this transformation process.

 

[Dale]

"In other words, the norm or magnitude of the four-velocity is always exactly equal to the speed of light. Thus all objects can be thought of as moving through spacetime at the speed of light. This provides a way of understanding time-dilation: as an object like a rocket accelerates from our perspective, it moves faster through space, but slower through time in order to keep the four-velocity constant. Thus to an observer, a clock on the rocket moves slower, as do the clocks in any reference frame that is not comoving with them. Light itself provides a special case- all of its motion is through space, so it does not have any "left over" four-velocity to move through time. Therefore light, and anything else traveling at light speed, do not experience the "flow" of time."

Please be aware that the four-velocity of light is undefined (division by 0). That is why you have to use an affine parameter instead of proper time for a photon. This means that you cannot use any reasoning based on the four-velocity to make any conclusions about light.

 

[ghwellsjr]

I predict the wikipedia article will soon be edited.

 

[phyti]

Checked out the wiki article better and man, it's pretty much exactly what I was talking about.
"In other words, the norm or magnitude of the four-velocity is always exactly equal to the speed of light. Thus all objects can be thought of as moving through spacetime at the speed of light. This provides a way of understanding time-dilation: as an object like a rocket accelerates from our perspective, it moves faster through space, but slower through time in order to keep the four-velocity constant. Thus to an observer, a clock on the rocket moves slower, as do the clocks in any reference frame that is not comoving with them. Light itself provides a special case- all of its motion is through space, so it does not have any "left over" four-velocity to move through time. Therefore light, and anything else traveling at light speed, do not experience the "flow" of time."

Motion is defined as change of position relative to a reference object in space. Motion in time can only be a metaphoric or poetic expression, the first being the case in the mathematical sense. The invariant interval is the distance between two events, and SR theory states that the time for light to travel that distance equals the distance divided by the speed of light, i.e., it's an equality. The interval must be invariant because physically events do not move. The time component ct is mathematically manipulated for the purpose of forming a uniform four component vector, which simplifies the math but obscures the reality.
All objects at rest moving through time at the speed of light is just another way of stating light speed is constant. Draw a circular arc of radius 1 from the vertical (time) axis to the horizontal (space) axis. Draw a line from the origin to a random point on the arc. The horizontal component represents the distance traveled, its end point indicates speed as fraction of c, and the vertical component represents the elapsed time for an observer moving at that speed.
To keep a proper perspective, the elapsed time is only on his clock, he is still vertically above the arc at t=1, i.e., 1 time unit has elapsed for all objects.
There is no need for objects to move through time, since the speed of light is constant and independent of its source, and that's sufficient to explain time dilation.
Some food for thought:
From 'The Meaning of Relativity', Albert Einstein, 1956:
page 1.
"The experiences of an individual appear to us arranged in a series of events; in this series the single events which we remember appear to be ordered according to the criteria of "earlier" and "later", which cannot be analysed further. There exists, therefore, for the individual, an I-time, or subjective time."
page 31.
"The non-divisibility of the four-dimensional continuum of events does not at all, however, involve the equivalence of the space coordinates with the time coordinate."
page 32.
"Finally, with Minkowski, we introduce in place of the real time co-ordinate l=ct, the imaginary time co-ordinate..."

 

[ghwellsjr]

I think you are confusing two different four-vectors: the one that was being discussed earlier is the four-velocity whose norm or magnitude is always c, and thus, not too useful. You are also mentioning the (spacetime) interval which produces the same value as the distance between two events no matter what frame of reference it is evaluated in.

 

[phyti]

I think you are confusing two different four-vectors: the one that was being discussed earlier is the four-velocity whose norm or magnitude is always c, and thus, not too useful. You are also mentioning the (spacetime) interval which produces the same value as the distance between two events no matter what frame of reference it is evaluated in.

His idea is not new and doesn't even work for a simple problem. If two objects with the same velocity are separated by a distance d, how does the 1st send a light signal to the 2nd if light only moves through space?

The primary point was reasoning that time is only a dimension in the mathematical sense.
Nothing moves through/in/along 'time'. Time is to observation what a metronome is to playing music, it provides the beat.

We have more than enough Harry Potter physics and science fiction.

 

[pervect]

The idea of moving through space-time was popularized by Brian Greene, a string theorist. The Wiki article was no doubt inspired from the same source, though it's hard to tell with Wiki. What's here today on Wiki is gone tomorrow - unfortunately it's not always a reliable source of information, though it's not awful.

While the idea of moving through space-time is a legitimate attempt to explain relativity in simple terms, many people dislike the explanation, which doesn't make much sense if you take it literally.

The particular problem is "moving through time". It makes sense as a metaphor, but when you start to think of it operationally, it's less clear, at least without some additional careful explanation.

If you stick to saying "the 4-velocity is always a unit vector", you won't create any misunderstandings or controversy, but you do risk getting a blank "huh" look from anyone who hasn't studied relativity.

 

[Godswitch]

I think what you are trying to illustrate is an old point about the observation of time e.g If time is only measured from one instance, you have to ask - Does time exist and if so how was time created etc

If all time is measured from a single event, in this case the big bang, then this is the age of the KNOWN universe. Looking through our telescopes we can see back through time, but is this merely an illusion and would it really matter...

Is the observed universe the same or different from the actual universe...or is what we see merely a moment of symmetry in an otherwise chaotic universe

The universe is expanding, so we believe, at a rate we do not know, if we were to build a super fast spaceship and travel in a single direction for any given time would the slowing down of the spaceship have an opposite effect on the rate at which time has passed for you the traveller [is time elastic?] and would this have an effect on the surrounding universe.

I think what this is to say is - Time for some things may seem to standstill but on closer examination this may not be the case!

 

[Simplyh]

phyti and pervect: you're quite right. Enough of trying to take magical conclusions out of mathematical developments ignoring its postulates, mathematical restrictions and assumptions.

 

[ghwellsjr]

His idea is not new and doesn't even work for a simple problem. If two objects with the same velocity are separated by a distance d, how does the 1st send a light signal to the 2nd if light only moves through space?

Whose idea? And what idea?

And I don't understand why you are asking the question. We could consider those two objects to be a rest in the same reference frame (whether or not the distance is the same d or a tranformed d, your question doesn't make that clear). So object 1 sends a light signal to object 2 and it travels at the speed of light across the distance (it moves through space)and gets there in the distance between them divided by the speed of light. What am I missing?