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Jaams
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A man suddenly decides to walk nearly at the speed of light. Without changing the length of his steps, will he need fewer steps to reach his destination?
Length of his steps in which frame of reference? His own, or that of the surface?Jaams said:Without changing the length of his steps
From his own perspective. All the man does is increase his pace.A.T. said:Length of his steps in which frame of reference? His own, or that of the surface?
pervect said:A man rides a bicycle at close to the speed of light. There is a tack on the tire that makes marks in the ground every revolution. As the man rides faster, the wheel expands, but he compensates for this by having an assistant measuring the length between tack marks in the cyclist frame after he gets up to speed.
Jaams said:I'm mostly interested in talking about the scenario purely from the perspective of length contraction, which says that his footprints should end up being further apart.. right? Yet an onlooker would say that the man taking longer steps is length contracted? This is where I'm stuck.
Once he gets on a "high speed" IFR of his walking, outer space contracts. He can reach far away galaxy in less than a short time of one step.Jaams said:A man suddenly decides to walk nearly at the speed of light. Without changing the length of his steps, will he need fewer steps to reach his destination?
A man suddenly decides to walk nearly at the speed of light. Without changing the length of his steps, will he need fewer steps to reach his destination?
Simon Bridge said:Since the traveller is moving, his stride is shorter (length contraction) and so you get more footprints between the start and finish of the journey - but - in the travellers frame, it is the distance from start to finish that is contracted, and so it takes fewer strides, so there should be fewer footprints.
Since the man has taken 3 steps over the ground with his left foot, left foot has moved 12 feet over the ground.ghwellsjr said:Since the man has taken 6 steps covering 4 feet each, the ground has moved 24 feet behind him in 30 nanoseconds confirming a speed of 80%c.
No, that's not right. The man can walk at any speed short of c. Look at the second diagram. The man's body is traveling at 80%c. His left foot (blue) travels at 97.561%c but for about 13.5/16.5 % of the time so it comes out to 80%c.jartsa said:Since the man has taken 3 steps over the ground with his left foot, left foot has moved 12 feet over the ground.
Man must stay near his left foot, which is covering the ground at speed 40%c, that's why man covers ground at speed 40%c.
The fact that there is also a right foot does not matter.
A conclusion from this: 50%c is the maximum walking speed.
I disagree. When walking, invariant time schedule of a foot is: half of the time on the ground, half of the time in the air.ghwellsjr said:No, that's not right. The man can walk at any speed short of c. Look at the second diagram. The man's body is traveling at 80%c. His left foot (blue) travels at 97.561%c but for about 13.5/16.5 % of the time so it comes out to 80%c.
True, as long as you're talking about the invariant Proper Time as depicted by the blue and red dots which is 3 nanoseconds on the ground and 3 nanoseconds in the air moving forward to the right as both my diagrams indicate.jartsa said:I disagree. When walking, invariant time schedule of a foot is: half of the time on the ground, half of the time in the air.
Yes, as long as all parts of your body are at rest with respect to each other. That's not the case with the walking man.jartsa said:An example of invariance of time schedules: I study physics 1 hour a day, astrology 3 hours a day, the ratio 1/3 is a frame independent invariant.
Half the time the left foot is pushing the ground behind the man and the other half the right foot is pushing the ground according to the man's rest frame. Look at the first diagram.jartsa said:When foot is in the air, it is moving over the ground. So we have: half of the time foot is moving over the ground, half of the time it is not moving over the ground. Those pauses cause a 50% decrease of average speed.
In the first diagram, the man is "taking a 24-foot walk" with six 4-foot steps, half with each foot.jartsa said:(I have always thought that when I walk 1 km, I take 1000 one meter steps. But actually I take 1000 two meter steps, 500 with each foot.)
I've tried to understand this scenario in a visual sense, but I don't know how to because I find poles and chalk markings to be too open for inaccurate interpretations. How does the onlooker notice that the spacing isn't the same (edit: How does it all add up)?pervect said:The ground observer notes that the spacing between marks is not the same (longer) than the spacing in the runner's reference frame. WHen he pays attention to the simultaneity issue, he finds they aren't simultaneous, either.
My goal is to be able to accurately understand and possibly explain relativity in the context of walking, so all approaches to this scenario are totally welcome.Simon Bridge said:The way this usually goes is that some sort of "paradox" is being set up like this:
The traveller leaves footprints in the ground.
Since the traveller is moving, his stride is shorter (length contraction) and so you get more footprints between the start and finish of the journey - but - in the travellers frame, it is the distance from start to finish that is contracted, and so it takes fewer strides, so there should be fewer footprints.
Is this what is intended here?
Often left out of relativity scenarios is how the observers find out that there is anything different.How does the onlooker notice that the spacing isn't the same (edit: How does it all add up)?
The process of walking is quite complicated, so it is not a useful way to make the details of relativity clear. It seems you don't have a clear question - which means that we are unlikely to be able to help you better than just working through a relativity text. You have seen a number of approaches above that will provide starting points.My goal is to be able to accurately understand and possibly explain relativity in the context of walking, so all approaches to this scenario are totally welcome.
... this bit, however, is a question about the apparent paradox I was wondering about.He can reach far away galaxy in less than a short time of one step.
If that's how length contraction works, how can an onlooker possibly see it as length contraction?
ghwellsjr said:Half the time the left foot is pushing the ground behind the man and the other half the right foot is pushing the ground according to the man's rest frame. Look at the first diagram.In the first diagram, the man is "taking a 24-foot walk" with six 4-foot steps, half with each foot.
Well let's see if we can get you unstuck.Jaams said:I'm mostly interested in talking about the scenario purely from the perspective of length contraction, which says that his footprints should end up being further apart.. right? Yet an onlooker would say that the man taking longer steps is length contracted? This is where I'm stuck.
Yes, and this gets tricky with "walking", because the racewalking distinction of "walking" from "running" is that at least one foot must be on the ground all the time. So the guy might be "walking" in his frame, but a judge standing on the ground will disqualify him for "running", based on his frame. Racewalking looks silly enough at the usual speeds, but close to c it would be just ridiculous.pervect said:The ground observer will NOT see the marks as being burned "at the same time" with this setup by the way, and this turns out to be a key point in the analysis.
I think I have to agree with you. I keep thinking of better ways to improve them. Here are my latest improvements. I have added notes on the diagrams to hopefully explain some of the confusing aspects.Simon Bridge said:In other words - the ground observer sees the man taking long leaps - allowing him to cover more ground despite his short stride.
I like the diagrams BTW.
People not used to them can have trouble reading them though.
Simon Bridge said:The way this usually goes is that some sort of "paradox" is being set up like this:
The traveller leaves footprints in the ground.
Since the traveller is moving, his stride is shorter (length contraction) and so you get more footprints between the start and finish of the journey - but - in the travellers frame, it is the distance from start to finish that is contracted, and so it takes fewer strides, so there should be fewer footprints.
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.ktx49 said: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
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.how could there be 2 different versions of an event in regards to a quantity such as the number of footprints?