# Is one of my legs not in Perfect Time Sinc with the Other?

Well, you all know that it is most probably true that one of your legs has moved more than the other, and the other less. I am not saying there is really much of a difference, since you move your legs about the same for each when you walk, and they take about the same steps each per walk, but that is the key word, "About". Nothing in the Universe is perfect, so we can Probably conclude that one of your legs has moved a bit more than the other in you lifetime.

So, does this mean that with The Theory of Relativity, one of your legs has gone farther into the future relative to a certain non moving point relative to Earth than the other has? If so, it may only be to the trillionths of the trillionth of a second, but still, that means maybe your leg will know to do something quicker in its time than the other leg will. Or, if the effects were very extreme, maybe one leg will appear not exactly on your body, or appear to move slower than you intended it to, but that would be strange, and maybe create a pardox of some sort because it is moving at a slower rate than you wanted it to, or faster, because your time dilates when it is moving. Actually, to rephrase that, it will move at a different time than you wanted it to, however you are moving just fine. If that is true, what will you see in the place of your leg? The ground, some flesh (Probably not), or maybe a rip in space, which would be very weird.

As always, thanks for reading and I would greatly appreciate any opinions from you guys.

PeterDonis
Mentor
Well, you all know that it is most probably true that one of your legs has moved more than the other, and the other less.

Each of your legs may have moved a slightly different *distance* through space, but that in itself won't cause any relativistic effects due to differential "rate of time flow". That is observed when objects move at different speeds, not when they move through different distances.

So, does this mean that with The Theory of Relativity, one of your legs has gone farther into the future relative to a certain non moving point relative to Earth than the other has?

If you mean, is it possible that each of your legs has experienced a slightly different lapse of time than the other, since some common "reference time" in the past, then yes, this is in principle possible. Your legs will probably not always have been moving at exactly the same speed, and the variations probably won't exactly cancel out in their effects. (Btw, I'm not sure exactly what you mean by "a certain non moving point relative to the Earth", or how it relates to the question. The possible different lapse of time for each leg due to moving at slightly different speeds is relative to some particular time in the past when both legs were at rest relative to each other. Both legs do not need to have been at the exact same point in space at that time--in fact they can't be since they're separate objects.)

However, that does not necessarily imply the other things you seem to think it does:

If so, it may only be to the trillionths of the trillionth of a second, but still, that means maybe your leg will know to do something quicker in its time than the other leg will.

No, that's something different; it has to do with how nerve impulses flow from your brain to each of your legs.

Or, if the effects were very extreme, maybe one leg will appear not exactly on your body

This would not happen; your leg is attached to your body in all reference frames, relative motion does not change that.

, or appear to move slower than you intended it to

This is in principle possible, since each leg might be moving relative to your head. But it's that relative motion--each leg relative to head--that matters here, not the motion of either leg relative to the other. Even in this case, however, it wouldn't be as simple as a leg just moving slower than you intended it to. There are other optical effects involved, such as relativistic Doppler shift and Penrose-Terrell rotation. See, for example, these pages:

http://en.wikipedia.org/wiki/Relativistic_Doppler_effect

http://en.wikipedia.org/wiki/Terrell_rotation

it will move at a different time than you wanted it to,

Again, if this happens, it will be due to the way nerve impulses flow from your brain to your leg, not the motion of the leg itself.

If that is true, what will you see in the place of your leg?

Again, your leg remains attached to your body in all reference frames. The motion of the leg doesn't affect that.

pervect
Staff Emeritus
One of your legs can age more - suppose you swing your right leg around a lot, and leave the other more stationary.

But this differential aging won't affect the synchrnoziation process in any cumulative fashion. Lets examine the synchorinzation process in a bit more detail, by considering a "signal" and what happens to it. Suppose someone tickles your foot, for example. The tickling excites nerves, which *slowly* propagate the signal to your brain.

Your brain has some complex algorithm for processing all these signals, and putting sensations in order, which to some extent takes into account these propagation delays, but is by no means perfect.

The net result of all the biology is a sense of "now" that your brain creates for you, synthesized by processing out-of-date information from your nerves and various sources.

Considering all the delays required for nerve propagation and interpretation of the signals, the relativistic effects are pretty much negligible. I would guess that many other effects (say possible temperature variations of nerve propagation speeds) would be much more important.

No, that's something different; it has to do with how nerve impulses flow from your brain to each of your legs.

Well, lets hypothetically say that the pulses through your nerves from your brain were instantaneous, ruling out the speed of light for that motion. Or, choose to say that every single nerve pulse took exactly the same amount of time to send the direction to your leg to move. I am not saying I have asked this question because I have experienced my leg moving when I didn't expect it to.

Would you then notice something about it if the time difference between one leg and the other was extreme due to much higher use of the other one.

Oh, and sorry about the certain non moving point on Earth thing, I was trying to be specific about a stationary thing like the ground, but then I remembered that the Earth is constantly moving, so the theory of relativity does play into that, but now I realize that it doesn't matter because every part of your body is moving at the same velocity of you sit perfectly still, sorry.

And thanks for another detailed explanation, and for those links :)

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PeterDonis
Mentor
Would you then notice something about it if the time difference between one leg and the other was extreme due to much higher use of the other one.

I would agree with pervect that what you would sense in this case would depend a lot more on details of neuroscience than on any relativistic effects. I also agree with him that one would not expect any cumulative effects from the difference in motion between the legs. Your brain would just learn and adapt to the signals coming in as best it could to keep you in reasonable control of your legs.

Oh, and sorry about the certain non moving point on Earth thing...

No problem, it's far better to do the best you can in expressing a question, even if it's not perfect, and then follow up with a dialogue to clarify as needed, than not to ask the question at all.

And thanks for another detailed explanation, and for those links :)

You're welcome!

pervect
Staff Emeritus
Well, lets hypothetically say that the pulses through your nerves from your brain were instantaneous, ruling out the speed of light for that motion. Or, choose to say that every single nerve pulse took exactly the same amount of time to send the direction to your leg to move. I am not saying I have asked this question because I have experienced my leg moving when I didn't expect it to.

Would you then notice something about it if the time difference between one leg and the other was extreme due to much higher use of the other one.

Oh, and sorry about the certain non moving point on Earth thing, I was trying to be specific about a stationary thing like the ground, but then I remembered that the Earth is constantly moving, so the theory of relativity does play into that, but now I realize that it doesn't matter because every part of your body is moving at the same velocity of you sit perfectly still, sorry.

And thanks for another detailed explanation, and for those links :)

There isn't such a thing as instantaneous signals in relativity - so you won't get anthing very useful trying to imagine them.

Imagining impossible things is a good way to confuse yourself.

Probably the best question to ask would be what happened if your nerve signals transmitted as fast as possible, which would be 'c'. I belive you'd find that a nerve signal forced to follow a nerve path at the speed of light would take longer than a broadcast signal travelling at 'c', due to the nerve path being longer. I.e. in an inertial frame, the broadcast signal would follow a straight line path, but the path followed by the signal following the nerve would not be straight, and longer than the first path.

It's doubtful that you'd still see any significant source of synchronization error for this at ay reasoable speed, but you can imagine that if it became an issue, your brain or software could be adapted to take the added propogation time properly into account.

DaveC426913
Gold Member
In its simplest form, you stand on a merry-go-round, with your left foot on the centre, and your right foot as far out as comfortable. You spin and spin and spin.

The cells in your right leg will, in principle, age slightly slower than the left - for the duration of the spin. Your brain would, if capable, sense signals from the right leg arriving slightly slower than the left.

Once you stop spinning however, the differential aging and signal transmission ceases. Each leg once again ages at the same rate, though now the left is slightly older than the right.

Your brain would, if capable, sense signals from the right leg arriving slightly slower than the left.
Like the signals arriving from the right leg, if the flow of blood into the right leg slowed down, wouldn't this violate the continuity equation?

DaveC426913
Gold Member
Like the signals arriving from the right leg, if the flow of blood into the right leg slowed down, wouldn't this violate the continuity equation?

No. The flow of blood into the leg would proceed at the same rate. From the "point of view" of the leg, the blood flow from the body would have increased.

Again, for late-arrivers to the thread: in principle.