A question about special relativity

[BadgerBadger92]

I have a question about special relativity, hopefully this isn’t a silly question.

If there are two things, one moving near the speed of light verses the ground, due to time dilation, wouldn’t the traveling body look like everything in it is moving slower according to the frame of reference on earth? Would it appear to be traveling slowly too?

Sorry if I am wording this question oddly, I’m not sure how else to word it

 

[A.T.]

one moving near the speed of light

Would it appear to be traveling slowly too?

It's either "moving near the speed of light" or "traveling slowly" relative to the Earth. It can't be both.

 

[BadgerBadger92]

Thanks for your reply. I do have one more question though

I get now that it will still look like it’s traveling very fast, but what about things in the moving frame of reference? Would they appear to move slowly?

Sorry if my question isn’t clear

 

[Ibix]

Thanks for your reply. I do have one more question though

I get now that it will still look like it’s traveling very fast, but what about things in the moving frame of reference? Would they appear to move slowly?

Sorry if my question isn’t clear

It depends what you mean by "slowly".

If you mean "if I, at rest on the ground, were to take a series of close-up pictures of the fast moving object 1s apart (using a series of stationary cameras spaced along the object's route) and somebody was sitting on the object waving would the images show that his arm hadn't moved much between shots?" then yes, he would be moving slowly in that sense. However, there could be tens of thousands of miles between successive cameras, so in that sense he is moving very quickly.

Avoiding this kind of confusion of language is why we tend to talk about clock rates (or, better, just use maths). Take the man's waving arm as an approximate clock, swinging backwards and forwards about once per second in his rest frame. You would measure the repeat time as longer (possibly much longer) than 1s, while still acknowledging that his hand is moving at a significant fraction of the speed of light.

 

[FactChecker]

what about things in the moving frame of reference? Would they appear to move slowly?

Good question. Yes. It is time itself that a "stationary" observer thinks is distorted in a fast-moving reference frame. Every process that depends on time appears to be slowed in the moving reference frame. The talk about "clocks" includes any process by which the progress of time can be measured.

For instance, in particle accelerators, the decay rate of the fast-moving particles is slower than a "stationary" rate. The particles in an accelerator last longer and go farther before decaying than they would otherwise.
The difference can be extreme: Pion particles in a collider go at nearly the speed of light but they only live briefly. In Earth-time, they should only travel for 27 feet before they decay. But they are going so fast and their time is slowed so much that they travel a quarter of a mile before they decay. See FermiLab: Einstein's Clocks

 

[Sagittarius A-Star]

I get now that it will still look like it’s traveling very fast, but what about things in the moving frame of reference? Would they appear to move slowly?

The calculation result depends on the direction of movement of things in the moving frame.

Assume the two coordinate systems in standard configuration.

The easiest case is the following:
If things in the "moving frame" ($F'$) move perpendicular to the direction of the relative velocity $v$ between the two frames (that means $u'_x=0$), then their perpendicular velocity-component is slower with reference to the "stationary frame" ($F$) by the time-dilation factor.

$u_y = u'_y \sqrt{1-v^2/c^2}$
$u_x=v$.

See under "Transformation of velocity", which contains also other cases:
https://en.wikipedia.org/wiki/Velocity-addition_formula#Standard_configuration

 

[FactChecker]

Would they appear to move slowly?

Appear to who? To a stationary observer, every process in the moving frame are slowed. On the other hand, to an observer in the non-accelerating, moving reference frame, he can assume he is stationary and all physical processes measured in his reference frame behave as though he was stationary.

 

[BadgerBadger92]

Appear to who? To a stationary observer, every process in the moving frame are slowed. On the other hand, to an observer in the non-accelerating, moving reference frame, he can assume he is stationary and all physical processes measured in his reference frame behave as though he was stationary.

I think this answers my question, thank you!

 

[A.T.]

The calculation result depends on the direction of movement of things in the moving frame.

Assume the two coordinate systems in standard configuration.

The easiest case is the following:
If things in the "moving frame" ($F'$) move perpendicular to the direction of the relative velocity $v$ between the two frames (that means $u'_x=0$), then their perpendicular velocity-component is slower with reference to the "stationary frame" ($F$) by the time-dilation factor.

$u_y = u'_y \sqrt{1-v^2/c^2}$
$u_x=v$.

See under "Transformation of velocity", which contains also other cases:
https://en.wikipedia.org/wiki/Velocity-addition_formula#Standard_configuration

It should be noted that no matter what the axis of the local motion in the rocket is, over an entire local motion cycle it is slowed by the same amount in the frame where the rocket moves. So even if the velocity addition formulas look different for parallel and orthogonal axis, once you make the local motion complete a cycle, the differences cancel out.

 

[Roberto Pavani]

I have a question about special relativity, hopefully this isn’t a silly question.

If there are two things, one moving near the speed of light verses the ground, due to time dilation, wouldn’t the traveling body look like everything in it is moving slower according to the frame of reference on earth? Would it appear to be traveling slowly too?

Sorry if I am wording this question oddly, I’m not sure how else to word it

A.T. gave an excellent answer in post #2, but perhaps the original question was even simpler than we made it: if a clock moves fast toward Earth and I see its hands moving slowly (time dilation), does that mean I also see the clock itself moving slowly?

The answer is no. Time dilation slows the hands of the clock; not the clock itself.
The clock still flies past you at 0.99c; but if you could peek at its face as it passes, you'd see the hands barely moving. The speed of the object through space and the speed of processes inside the object are two completely different things, and only the second one is affected by time dilation.