Will Distance Between Footsteps Change When Walking Near Light Speed?

[ghwellsjr]

this is interesting.
however, the answers provided so far have been difficult for me to dissect...so let's simplify things and say the traveller only has one leg and hops around leaving just one footprint per "stride".

how would the number of footprints compare in the 2 different reference frames in the one-legged scenario(in layman's terms)?

thanks

You think that simplifies things? I'm afraid not. At least not with your brief description of what happens. You MUST provide all details to make your scenario unambiguous.

Instead of changing the scenario, why don't you ask questions about the scenario the OP presented and see if you can understand it.

 

[ktx49]

well in the context of the quote I provided, I assumed it would in fact simplify things, particularly in regards to the number of footprints in the different frames.

many of the replies to the OPs scenario seem(at least to me) to be centered around how contraction would change the distance of the stride...and while its certainly interesting, I found Simon's particular "version" of the paradox to be a little easier to digest and even more intriguing. ie. how could there be 2 different versions of an event in regards to a quantity such as the number of footprints?

sorry if this is fundamentally a different question than the OPs, as I did not mean to hijack or derail the thread...as i said, it just seemed much more paradoxical to have a disagreement on the number of footprints as compared to a disagreement on the distance between footsteps. because of this, I thought(incorrectly?) that a single-legged man may simplify things yet still encompass the basic premise of the paradox.

does that help? and if my questions are indeed a much different problem from the OPs, I will gladly move my discussion to a new thread to prevent hijack.

 

[Simon Bridge]

how could there be 2 different versions of an event in regards to a quantity such as the number of footprints?

All observers agree about how many footprints there are on the ground at the end of the journey - but they disagree about the details of how they got there. That's how the apparent paradox is resolved.

Define: The spacing between footprints is the length of each step taken.
Define: The distance between feet when both are on the ground is the length of the stride.
In the walker's reference frame, these two lengths are the same.

The apparent paradox arises because the problem is phrased so we'd expect the two to be the same in all reference frames ... but this is not correct.
The proper stride-length is measured in the reference frame of the walker, while the proper step length is measured in the reference frame of the ground. Looked at this way, you'd expect the stride to be smaller than or equal to the step.

If you want to try for a hopping-type problem, you should start a different thread.
Meantime you should check out the links provided earlier.

 

[frish]

Amazing hoe a simple question can produce such a wealth of answers.

The number of steps remain the same. The distance to walk and size of the step do change
same way when observed in different frames. Obviously.
Also, imagine a distant , moving, observer viewing the walk. Distances would be changed
but observed steps are same.

 

[Simon Bridge]

The number of steps taken to cross the distance would be the same - but how the person walks is observer dependent.
Nobody sees anything weird or non-physical though, and nobody will be aware that anything funny is happening until they compare notes with other observers.

 

[sweet springs]

The conveyers we use in the airports to reach the terminal in short time gives us an example. One step distance for the walker and that of waiting passengers in the cue for boarding are different though they count the same step numbers. Is it a good example though not relativistic?

 

[ghwellsjr]

well in the context of the quote I provided, I assumed it would in fact simplify things, particularly in regards to the number of footprints in the different frames.

many of the replies to the OPs scenario seem(at least to me) to be centered around how contraction would change the distance of the stride...and while its certainly interesting, I found Simon's particular "version" of the paradox to be a little easier to digest and even more intriguing. ie. how could there be 2 different versions of an event in regards to a quantity such as the number of footprints?

I hope you realize that when Simon articulated the paradox in post #11, he wasn't resolving it.

I think the issue can be clearly understood if you look at his definition of "stride" in post #33: It's the distance between the two feet when both are on the ground (at the same time). There're two things we can take from this. First, a one-legged man cannot have a stride and second, the stride only exists (at least for my examples) in the man's rest frame, in the ground frame both feet are never on the ground at the same time.

I unfortunately didn't follow this advice in my post #15 where I said the stride increased from 4 feet to 6.67 feet. I should have said the spacing of the footprints increased from 4 feet to 6.67 feet. I hope my error didn't contribute to any confusion.