It seems strange to equate this with time in Special relativity.
No arguments there. It takes everybody that way.
It is a well-known fact that being strange is not the same as being wrong. This probably isn't the first time you have encountered something new and strange that is also true... it certainly won't be the last.
We cannot rely as much as we'd like on our intuitive feel for what is true - which is why we do experiments.
The Universe simply does not care about what we find strange.I like Dr Greg's response - you may find it easier to grasp relativity by analogy to rotations.
yuiop said:
When an object is far away it appears smaller, but when we bring it back we see that its physical size is unchanged.
What you are saying is that the "proper length" of an object is that measured by a ruler that is in the same place as the object.
It is not so much that the length is "position dependent", but that the initial description failed to properly take into account the relationships between dimensions.
We are used to thinking of time and distance as being different things - independent.
When we do this, we fail to properly take into account the relationship between them.
The apparent change in size is an optical effect but there is no tangible physical change in the size of the object.
We are used to thinking of the "real size" and "apparent size" like this because perspective is a common phenomenon that we have evolved to deal with - but perspective is not an optical illusion: it is how geometry works in 3D.
The velocity stuff is what happens when you try to extend the concept of perspective to 4D space-time.
In special relativity, the proper length of an object is that measured by a ruler that is right next to it
and is at rest wrt the object.
For example in the twins paradox, the traveling upon return is tangibly younger than the twin that remained behind. The time dilation is not just ephemeral phenomena that only exists when when a object is moving, as you appear to be suggesting, but cumulative and can be measured directly by comparing clocks that have taken different paths through spacetime by bringing them back alongside each other. Short lived particles in a high speed centrifuge live longer than identical particles that remain at rest. How do you explain this, if time is not velocity dependent?
In the above descriptions you have implicitly taken an absolute reference frame.
This is a habit you will have to get out of - to really appreciate the twin's paradox, you need to look at it from the POV of both twins.
But I don't want you to think that I mean the transformations of relativity are some sort of illusion.
We could perhaps make a case that the time dilation of the particles in the centrifuge is a function of centrifugal force, but I suspect you are saying that there is no cause of time dilation because time dilation is not a real physical effect. Am I understanding you correctly?
I was trying to build to the idea that time and space are both aspects of a greater whole - time dilation and length contraction are what happens when you look at just one and neglect the other dimensions. They are effects of geometry: like height and width in DrGreg's analogy.
time and space do not depend on velocity -
they depend on each other.
it is how different observers see the same phenomena that depends on their
relative velocities.As far as the particles in the centrifuge are concerned, they live just as long as always. Nothing has changed. It's just that when you compare their clocks with the ones in the lab that you see a difference. Their time did not slow down for them, their time slowed down for everyone in the lab.
Changing velocity does to the length of a rod what moving further away from it does.
In the latter case we have senses that are equipped to notice the extra dimension that changed - in the former we do not, so the latter is intuitively easy to understand and the former is not.
The intuitive feel for relativity comes with practice.
This is where I usually post the following crash course on the concepts:
http://www.physicsguy.com/ftl/html/FTL_intro.html
section 1.2 should help.
