Understanding Relativity: Increasing Speed

[neolayman]

Hi, I have only had a personal interest in physics so far and have yet to complete so much as one basic introductory physics course. I'm in second semester calculus, so I'm not hopeless on some fronts of understanding terms or mathematical ideas, but I have yet to understand what a manifold is.

I'm always comming to a stand still when I consider the concept or time being relative and that one object moving at or near the speed of light ages more slowly than an object that is nearly at rest (or was relativity claiming to elliminate rest completely?).

The real trouble that I have in understanding this is the idea that at some point of increased speed, an object might be moving relativly slower from the observer that is closer to being at rest (is there a term for this that I would be able to read up on?). Would it then be possible in theory for an object to move two feet so quickly that the obverver only sees it move incredibly slowly and taking billions of years to get from point A to point B? Or would the moving object simply dissappear only to reappear at the targeted point in space but way into the future as though all movement were essentially a teleport to a future point in space? Or if subspace is a spatial plain that holds while a direct structured space retains the ability to bend, then would there similarly be a subtime?

I realize that i must have many clear misconceptions here, but I'd like to be corrected in them so as to have a clearer idea in mind of what is known or postulated in physics today.

 

[Hootenanny]

Welcome to the fourms neolayman,

An good place to start would be to consider the lorentz transformations. However, if you are having difficulty getting your head around the lorentz transformations it may be easier to start with the galilean transformations, which are low speed approximations. I've inlcuded a few references below;

http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html" - a good general physics reference
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/ltrans.html#c1"
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/ltrans.html#c2"

Once you've read up and understood the lorentz transformations, you could move on to time dilation and length contraction.

 

[JesseM]

I'm always comming to a stand still when I consider the concept or time being relative and that one object moving at or near the speed of light ages more slowly than an object that is nearly at rest (or was relativity claiming to elliminate rest completely?).

In relativity you can only talk about speed relative to a particular frame of reference. So if you're traveling at a significant fraction of the speed of light relative to me, then I'll measure your clock to be running slow in my own rest frame; but by the same token, you will measure my clock to be running slow in your own rest frame, since in that frame it's you who's at rest and me who's moving at a significant fraction of light speed (speed is symmetrical, so that if I measure you to be traveling at speed v in my rest frame, you also measure me to be traveling at speed v in your rest frame).

The real trouble that I have in understanding this is the idea that at some point of increased speed, an object might be moving relativly slower from the observer that is closer to being at rest (is there a term for this that I would be able to read up on?).

No, it doesn't work that way, the time dilation effect just means that I'll measure any physical process which can be treated as a clock (for example, the regular oscillations of cesium atoms) to run slower if it's moving relative to me, but speed always works in a straightforward way--if something is moving at 0.8c relative to me, that means I'll measure it to move 0.8 light-years in 1 year, as measured by my clocks and rulers (and of course my clocks seem to be running at the correct rate from my perspective).

Or if subspace is a spatial plain that holds while a direct structured space retains the ability to bend, then would there similarly be a subtime?

No such thing as "subspace" in relativity, that's just something invented by Star Trek.

 

[neolayman]

Thank you Jessie, these explanations are very helpful.

In relativity you can only talk about speed relative to a particular frame of reference. So if you're traveling at a significant fraction of the speed of light relative to me, then I'll measure your clock to be running slow in my own rest frame; but by the same token, you will measure my clock to be running slow in your own rest frame, since in that frame it's you who's at rest and me who's moving at a significant fraction of light speed (speed is symmetrical, so that if I measure you to be traveling at speed v in my rest frame, you also measure me to be traveling at speed v in your rest frame).

Ok, so then, when we say that speed is symmetrical to the observer (right?) then we are saying that light and waves are the only things that are always moving at a speed constant relative to space itself (because the speed of light never changes, even when pushed or slowed relative to a specific point in space?)? Then by that token, light and waves are also moving with a time that is absolute to space as well right?

Also, something else still confuses me about the idea that the times of both objects are relativly different. If they are only relatively moving away from one another, then why would one object retain a difference in time that the other doesn't? One's time moves quickly while the other's time moves slowly right? Why, and what determines the slower?

No such thing as "subspace" in relativity, that's just something invented by Star Trek.

Thanks for pointing that out. I'll steer away from the term from now on, but is there something else to describe what I mean? That as space 'bends', an actual absolute space would theoretically be where the bending space would otherwise be thought to have been if the space weren't bent (right?).

 

[pervect]

Ok, so then, when we say that speed is symmetrical to the observer (right?) then we are saying that light and waves are the only things that are always moving at a speed constant relative to space itself (because the speed of light never changes, even when pushed or slowed relative to a specific point in space?)? Then by that token, light and waves are also moving with a time that is absolute to space as well right?

Light moves at a constant speed relative to any observer you choose. I don't think it makes much sense to even talk about the speed of something "relative to space" - no experimental way of determining this comes to mind.

Also, light does not experience time as we know it. This has come up before in many threads on the "perspective of a photon". Unfortunately, a photon does not have a perspective based on time, if it has one at all. (There are some rather abstract senses in which it might be possible to say that a photon has a perspective).

I would recommend taking a step back, forgetting about velocities "relative to space", and thinking about things we can actually measure. What we can actually measure are time intervals and distances from physical observers (i.e. observers who move less than 'c' according to relativity). Different physical observers measure different velocities and coordinates, and relativity tells us how to translate the results from one observer into the viewpoint of another. (The process is different than one would expect from classical physics).

Special relativity also points out that any physical observer will measure the velocity of another physical observer as being less than 'c'.

 

[MeJennifer]

I don't think it makes much sense to even talk about the speed of something "relative to space" - no experimental way of determining this comes to mind.

I fully agree with you.

As an aside: this notion however is sometimes presented in cosmology in relation to the expansion of space.

This has come up before in many threads on the "perspective of a photon". Unfortunately, a photon does not have a perspective based on time, if it has one at all. (There are some rather abstract senses in which it might be possible to say that a photon has a perspective).

I disagree, a photon is also a wave, and a wave is a pretty good clock!

When the photon "travels" between an emitting and absorbing event his "clock" stands still.

As far as I know, and assuming the objects are at rest relative to each other, the phase of the emmitting and of the absorbing event are always identical, but perhaps a QM person could confirm the validity of these statements.

 

[neolayman]

I fully agree with you.

As an aside: this notion however is sometimes presented in cosmology in relation to the expansion of space.

It sounds as though I'm either using the word 'relative' incorrectly or that you are saying that space as a courier of matter may as well not exist, but then at the same time, what one might see as a point in space or a vacuum in space is actually like another piece of matter which has it's own time dilation-like process. So far, I'm curious if all of the responses I'm getting here are agreeing perspetives in physics, cause this is very confusing. Are there any hypotheticals that could describe things well?

Like say if two stars were colliding (Their systems and all) and on two sides of this event, set perpendicular to the line that goes through the nuclei of both stars, are groups of physicists and astronomers studying the collision (ship A and ship B). Let's also assume that their communications breach the distance between them, as if their signals went through wormholes to get to one another. On one side, ship A realizes that they are out of coffee and sends an assistant to go get a load from their docking station that is, let's say twice the distance from the line that goes through the two stars, than ship A and ship B (this distance equals the distance between ship A and ship B just to be clear about the picture so far, but this is all for reference to explain things, since this isn't a geometry question). To get to the docking station efficiently, is there an ideal speed to travel? If he goes half the speed of light, would he be defeating the purpose? Also, let's say that Ship B hears from ship A that they sent out for coffee. Since they are relatively at rest from one another, ship A and ship B would not have a dilation in time from one another right? So, their communications are fine, but then each one wishes to contact the assistant to let him know that ship B also wants coffee. When they contact the assistant, is his voice slowed because he is moving away rom them? Are ship A's and ship B's voices sounding quickened to the assistant?

It's probably really silly to all of you and full of misconceptions. If there is another reference or even a science fiction book that describes things in this much real detail or better, that should work for me just as good.

Also, I'm wondering if anyone knows where I can reference the time that it takes for two stars to collide, two galaxies to collide, and the time that it takes for the main event of a super nova and a gamma ray burst to occur. Wikipedia let me down on those facts so I don't know where else to look.

I disagree, a photon is also a wave, and a wave is a pretty good clock!

When the photon "travels" between an emitting and absorbing event his "clock" stands still.

Wouldn't that mean that the distance between any emitting and absorbing event doesn't even complete one light wavelength?

 

[pervect]

It sounds as though I'm either using the word 'relative' incorrectly or that you are saying that space as a courier of matter may as well not exist, but then at the same time, what one might see as a point in space or a vacuum in space is actually like another piece of matter which has it's own time dilation-like process. So far, I'm curious if all of the responses I'm getting here are agreeing perspetives in physics, cause this is very confusing. Are there any hypotheticals that could describe things well?

Space may or may not "exist" in some abstract sense. The impression that I'm getting is that you are thinking of space as some sort of "ether".

The point I'm trying to make is that attempting to define a velocity relative to "space" i.e. the ether is at best a useless concept, and will probably end up confusing you.

It is a useless concept because relativity predicts it can never be measured. Like many matters of philosophy, it is possible to "hang on" to the idea that there is an ether - it's not quite an error to believe that there is an ether. It is an error, though, to believe that one's velocity relative to this ether can be detected experimentally. Relativity finds this to be impossible.

Since it can't be detected experimentally, by far the easiest way to learn relativity is to forget about the idea of an ether, and start focusing on what actual physical observers measure.

There are a very few people who believe in some sort of "ether" that can do relativity correctly (John Bell comes to mind), but most people who start out with this view never really learn relativity correctly and get stuck somewhere along the way with various misconceptions.

BTW, when I say one can "do relativity correctly", I mean that one can work problems in relativity and get the same results as everyone else (i.e. get the mainstream results).

 

[neolayman]

Space may or may not "exist" in some abstract sense. The impression that I'm getting is that you are thinking of space as some sort of "ether".

The point I'm trying to make is that attempting to define a velocity relative to "space" i.e. the ether is at best a useless concept, and will probably end up confusing you.

Ok, I think I understand what you are saying. Ether would be one way to put it. More directly my own theory of physics from what little I know can only go so far as to think that space and time in reality are just like space and time in a computer simulation. There's the data of where things can be (space) along with the data of what fills certain positions, and when animated, each moment in time is a set frame of data (I don't think that this idea is necessarily correct at all, but it is the most likely understanding and means of understanding by my own knowledge so far, hense the want to elliminate these confusions). This of course assumes that time and space are finitely divisible at some point.

Provability is irrelevant since it's just a thought of what's possible. It's all the better for my goals that it's not yet disproven or provable, but asside from that I do need to know what evidence shows of the scenario I mapped out above or something similar. I at least need to know what would happen if someone were to set out and move relativly close to the speed of light from a starting point, and had direct communication with someone at that starting point. Would the communication be slowed to one and the other quickened? If so, what determines one or the other?

Also I understand that you are pointing out the difference between the science and the mataphysical philosophy surounding this subject. I think that I might have misplaced this thread in that sense, but I do want real evidence and understanding of that evidence to work with.

 

[JesseM]

Ok, so then, when we say that speed is symmetrical to the observer (right?) then we are saying that light and waves are the only things that are always moving at a speed constant relative to space itself (because the speed of light never changes, even when pushed or slowed relative to a specific point in space?)? Then by that token, light and waves are also moving with a time that is absolute to space as well right?

As others have said, I don't think it really makes sense to say that light moves at the same speed relative to "space". When physicists refer to the speed of light as a constant, what this means is that if something's (change in position)/(change in time) = c in one inertial reference frame, and then you find the position and time coordinates of the same measurements in a new inertial reference frame and recalculate (change in position)/(change in time) in the new coordinate system, the answer will still be c. This will not be true of speeds other than c. In general, if I measure on object moving at speed v relative to me, and you measure me to be moving at speed u relative to you (with both the object and me moving in the same direction relative to you), then you will measure the object's speed to be w = (u + v)/(1 + u*v/c^2), the formula for addition of relativistic velocities. If v=c then w=c too, regardless of u, but if v is smaller than c, then w will be different than v.

Also, something else still confuses me about the idea that the times of both objects are relativly different. If they are only relatively moving away from one another, then why would one object retain a difference in time that the other doesn't? One's time moves quickly while the other's time moves slowly right?

No, as long as each moves inertially (constant speed and direction, no acceleration), then each one will measure the other one's clock to be running slower than their own, in their own inertial rest frame. You might want to take a look at my illustration of two ruler-clock systems moving alongside each other at constant velocity in this thread.

Thanks for pointing that out. I'll steer away from the term from now on, but is there something else to describe what I mean? That as space 'bends', an actual absolute space would theoretically be where the bending space would otherwise be thought to have been if the space weren't bent (right?).

If you're just interested in questions about how objects in relative motion appear in one another's frames, this is just a special relativity question, spacetime curvature only appears in general relativity when you want to take into account the effects of gravity. In general relativity it's spacetime that bends, and the "bending" is described mathematically using purely intrinsic quantities that could be measured by a being confined to the spacetime surface, with no reference to any higher-dimensional "embedding space" for the object to sit it. In terms of your computer simulation analogy, if one wanted to simulated how things move on a curved surface, one could either describe the curvature by having the computer keep track of the position of each point on the surface in some higher-dimensional coordinate system, or on could use the sorts of purely intrinsic ways of defining curvature that I mentioned, in which case the computer would only keep track of the curvature at each point on the surface (using some sort of curvature tensor), with no variables representing the position of the curved surface in any higher-dimensional space.