What are speeds and time relative to?

[gaz_hayes]

Hi all,

 

I was just wondering if someone can explain this to me.

 

If [mass increases] and [speed of time decreases] as speed increases, what is the speed relative to?

 

Can there ever be absolute rest?

 

If something is at absolute rest, what happens to the speed of time (to outside observers), or is it just relative to the outside observer's speed? And what about the mass of the object at rest? Can mass just disappear when an object slows down enough (is mass created by speed)?

 

If everything is just relative, then where does mass fit in? I can understand with time because time 'appears' no to change for the objects that are changing speed, but the change in mass is actually observable to the object that is changing speed, right?

 

Also, to an outside observer (moving), something moving at speed y along a body that is at rest would appear to be moving faster than y due to time having been sped up to that observer. If that is the case, then what is speed y in terms of mass/time? Is it the speed to the outside observer or the object at rest?

Edited June 1, 2011 by gaz_hayes

[lemur]

There are people with equations here that can probably answer your question precisely. I just want to point out that nothing can really be totally at rest insofar as it has to move relative to other things in the universe. So, in that sense speed, or rather acceleration, is relative to the gravity an object faces, however distant and weak the source of that gravity may be.

[swansont]

The speed is relative to some other frame of reference. Normally, since all inertial reference frames are equivalent, the observer assumes him/herself to be at rest. Some object in another frame would be moving with respect to the observer. There is no absolute rest, since there is no physics test that can show that you are at rest and another is moving at a constant velocity, or vice-versa.

 

The change in mass depends on the definition of mass. If it is (re)defined to be a proxy for energy, then it varies just as kinetic energy varies depending on your frame. There are definitions of mass that do not depend on the reference frame (rest mass, invariant mass). One has to be careful not to mix these definitions when discussing the topic.

[timo]

If [mass increases] and [speed of time decreases] as speed increases, what is the speed relative to?

Speed is measured relative to something that is defined as "at rest"; usually a physical object. For example, the speed of a car is often measured relative to the road, which is defined at rest (note that in some cases it may be more suitable to measure the speed of a car relative to that of another car; when determining how long it takes the cars to overtake another, for example). This statement has nothing to do with the first part of your sentence. This is because the first part is highly questionable; without a context it is somewhere between content-free and wrong (or does it make any sense to you?).

 

Can there ever be absolute rest?

Do you know how mathematicians capture lions? They build a cage, lock themselves in it, and declare "this is outside". Point is: you can define a lot of things if you really push it - and are willing to sacrifice sensibility. One usually assumes that there is no sensible "absolute rest".

 

 

If everything is just relative, then where does mass fit in?

"Everything is relative" does not follow from velocity being relative (and it's very far from the viewpoint of modern physics, in case that matters).

[DrRocket]

Hi all,

 

I was just wondering if someone can explain this to me.

 

If [mass increases] and [speed of time decreases] as speed increases, what is the speed relative to?

 

Can there ever be absolute rest?

 

If something is at absolute rest, what happens to the speed of time (to outside observers), or is it just relative to the outside observer's speed? And what about the mass of the object at rest? Can mass just disappear when an object slows down enough (is mass created by speed)?

 

If everything is just relative, then where does mass fit in? I can understand with time because time 'appears' no to change for the objects that are changing speed, but the change in mass is actually observable to the object that is changing speed, right?

 

Also, to an outside observer (moving), something moving at speed y along a body that is at rest would appear to be moving faster than y due to time having been sped up to that observer. If that is the case, then what is speed y in terms of mass/time? Is it the speed to the outside observer or the object at rest?

 

 

There is no such thing as "speed of time". "Speed of something" is "change in something"'/"change in time". "change in time"/"change in time" = 1, always.

 

What relativity tells us is that observers in relative motion to one another have different notions of both time and space -- time and space are not the absolute notions of everyday experience, but are dependent on the observer. What is invariant is a more abstract notion -- spacetime and the "spacetime interval" ([math](spacetime \ interval)^2 = ( \Delta t )^2 - (\Delta x)^2 - (\Delta y)^2 - (\Delta z)^2[/math]). The spacetime interval is neither time nor space, but a combination of both and it is differences in how that interval is partitioned into time and space separately that result in the "time dilation" and "length contraction" of elementary special relativity. Lorentz transformations preserve the spacetime interval, but change the partition.

 

Speed is relative between the reference frames of two observers.

 

Observers will agree on the speed of light. There is nothing magic about it being light. If you look carefully at the physical derivation of the Lorentz transformations, you will find that if you postulate that some phenomenon, any phenomenon, propagates at some speed "x" in all inertial reference frames, the you get the Lorentz transformations with "x" in place of the usual "c". There can be only one such speed "x". One the notes the experimental fact that light propagates at "c" in all inertial frames, and, voilà, you have special relativity in the usual form.

 

"Mass", in the form of "relativistic mass depends on the observer. You cannot determine the speed of an object relative to you by measuring the mass, but you can if you know the ratio of the relativistic mass to the rest mass. For macroscopic objects you can do this if you replace "rest mass" with "invariant mass", which is relativistic mass in center-of-momentum coordinates.

 

"Mass" is not the well-defined concept that you might think. There are several notions of mass, all valid and all different. There was a thread on this topic recently. As a result I had a conversation on the subject with a local prize-winning (not the Nobel prize, but a nice one anyway) high-energy physicist friend. He went so far as to point out that not only are rest mass, invariant mass and relativistic mass all valid and useful in their place, but also even in Newtonian mechanics it is a happy, but not logically required, coincidence that inertial mass and gravitational mass are equal.

 

There is no such thing as "absolute rest". That is fundamental to special relativity.

[gaz_hayes]

Thanks everyone!

 

Especially DrRocket, you gave me the "ah huh" moment.