# Time dependent on velocity?

#### cooper607

i have the basic question of special relativity why time , length and mass is a function of velocity here? i may know the mathematical interpretation of special relativity but i did not understand it physically how time can depend on these parameters. some plz make me clear on this issue
regards

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#### Simon Bridge

Homework Helper
Simple answer: they don't depend on velocity.
If I have a 1m long stick, it will stay 1m long no matter what speed I am doing - so long as I'm carrying the stick with me.
But if I leave it behind, the the length I measure it as depends on how fast it is going.
(In relativity, the observer is always stationary.)

You understand how two people can measure a different value for the velocity of some object right?
You understand how distant objects get smaller?
It's the same reason for time and distance...

#### pervect

Staff Emeritus
i have the basic question of special relativity why time , length and mass is a function of velocity here? i may know the mathematical interpretation of special relativity but i did not understand it physically how time can depend on these parameters. some plz make me clear on this issue
regards
I would describe time and length as observer dependent rather than "a function of velocity", though this may just be a personal preference.

It might be helpful to focus on the Lorentz interval, which is basically sqrt(length^2 - time^2), and note that the Lorentz interval is what is independent of the observer (and the observer's velocity) in special relataivity.

Given that the Lorentz interval is invariant, it is useful to know how to use the invariant Lorentz interval to find time and length given a specific observer. For the non-rotating observer, specifying surfaces of constant time is sufficient to translate the notion of the interval into times and lengths.

#### yuiop

Simple answer: they don't depend on velocity.
If I have a 1m long stick, it will stay 1m long no matter what speed I am doing - so long as I'm carrying the stick with me...
... You understand how distant objects get smaller?
It's the same reason for time and distance...
When an object is far away it appears smaller, but when we bring it back we see that its physical size is unchanged. The apparent change in size is an optical effect but there is no tangible physical change in the size of the object. It seems strange to equate this with time in Special relativity. For example in the twins paradox, the travelling 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? 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?

#### DrGreg

Gold Member
i have the basic question of special relativity why time , length and mass is a function of velocity here? i may know the mathematical interpretation of special relativity but i did not understand it physically how time can depend on these parameters.
Suppose I have a 1-metre-long rod. If I hold it vertically it is 1 metre high and, say, 1 cm wide. If I hold it horizontally it is 1 metre wide and 1 cm high. If I hold it at an angle of 45 degrees, it is about 70 cm high and 70 cm wide. Throughout all this, the length of the rod remains a constant 1 metre, but its width and height vary.

Now suppose I asked you "why height and width is a function of angle here? I may know the mathematical interpretation of geometry, but I did not understand it physically how height can depend on this parameter." What sort of answer would you accept?

#### Simon Bridge

Homework Helper
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.

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 travelling 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.

#### WannabeNewton

]It seems strange to equate this with time in Special relativity.
I agree completely. Optical illusions and physical rotations are on a completely different playing field from Lorentz transformations so the analogy is somewhat misplaced.

Actually this was already discussed more or less in a previous thread, https://www.physicsforums.com/showthread.php?t=742431, so that might serve as a useful reference.

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#### pervect

Staff Emeritus
I don't think comparing the Lorentz transform to a physical rotation for pedagogical purposes is odd at all. Consider the "parable of the surveyors" from Taylor & Wheeler's "Spacetime Physics". The first chapter of the 1965 edition, which basically takes this approach, can be downloaded from Taylor's website from a link at http://www.eftaylor.com/download.html#special_relativity

#### Simon Bridge

Homework Helper
I agree completely. Optical illusions and physical rotations are on a completely different playing field from Lorentz transformations so the analogy is somewhat misplaced.
That's the trouble with tackling this with analogies.
The rotation one is very common - the trick is to emphasize the useful part.
I suspect OP may be thinking of velocity as an absolute anyway.

Actually this was already discussed more or less in a previous thread, https://www.physicsforums.com/showthread.php?t=742431, so that might serve as a useful reference.
... oooh neat. Thanks.
Doesn't really help OP's question though...

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#### Dale

Mentor
i have the basic question of special relativity why time , length and mass is a function of velocity here? i may know the mathematical interpretation of special relativity but i did not understand it physically how time can depend on these parameters.
In relativity the answer to any "why" question is the two postulates of SR. All relativistic effects stem from the two postulates:

1) the laws of physics are the same in every inertial frame
2) the speed of light is the same in every inertial frame

Those two postulates logically imply that time and length are a function of velocity. Einstein derived that fact in his original paper, but you can find many derivations.

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