Grabbing Hands at Speed of Light: What Happens?

[JBou]

So someone is passing by me at ~the speed of light, which I believe would make them appear to be stationary from my point of reference. I decide to reach out and grab their hand. What happens?

 

[PeterDonis]

which I believe would make them appear to be stationary from my point of reference

Why do you believe that? How can something be moving past you at almost the speed of light and also appear stationary? That doesn't make sense.

It is true that a clock being carried by the object passing you at almost the speed of light would appear to be ticking very slowly, compared to yours. But that's not the same as "appearing stationary".

 

[HallsofIvy]

So someone is passing by me at ~the speed of light, which I believe would make them appear to be stationary from my point of reference.

What? No, if he is approaching you at the speed of light, he certainly is not, and would not "appear", stationary relative to you!
Where did you get this idea?
(Of course, a person cannot approach you "at the speed of light" so I am assuming you mean something like "99.99% of the speed of light.)

I decide to reach out and grab their hand. What happens?

Best outcome- his hand immediately slips out of yours. Worst scenario- both your hands get ripped off!

 

[JBou]

okay then... if his clock is moving slowly, doesn't that mean he would appear to be moving slowly?

 

[Ibix]

It isn't possible for anything with mass to travel at the speed of light. Someone traveling just below the speed of light would be be traveling very fast, but their movements would be slow - their watch would be ticking slowly from your perspective.

Assuming your grip held, you would accelerate and the other guy would slow down. You'd end up at rest with respect to each other (and your watches will be ticking at the same rate). But you'd both be moving with respect to people you were originally at rest next to. The exact speed depends on your masses - relativity modifies the familiar Newtonian laws of conservation of momentum and energy, but does not repeal them.

 

[PeterDonis]

if his clock is moving slowly, doesn't that mean he would appear to be moving slowly?

"Moving slowly" in what sense? He's moving past you at almost the speed of light. You need to be more specific about exactly what you are describing.

 

[JBou]

I guess I just remember reading that if you were to watch an object approach the speed of light (I know its not possible), it would appear to slow down. Maybe I am mistaken.

 

[DaveC426913]

They are traveling at almost the speed of light past you, but you observe them time-dilated, which means they are essentially frozen within that moving frame.

It is unfortunate that we use the same words to describe someone "moving" relative to you as someone "moving" their own body.

 

[PeterDonis]

I guess I just remember reading that if you were to watch an object approach the speed of light (I know its not possible), it would appear to slow down.

Once again, "slow down" is too vague. What, specifically, would you expect to observe?

I have given one specific example: that the clock carried by the object would appear to tick slowly compared to yours. But that can be observed even though the object itself is moving past you at nearly the speed of light. So the clock appears to "slow down", but the object's motion relative to you does not.

If you are thinking of something else "slowing down", what?

 

[Ibix]

If our hero is pacing up and down in his rocket ship, his paces (and watch, aging, brain function, metabolism, etc) will be slow compared to yours (at least from your perspective - he'd say the same about you). However his rocket ship will be doing whatever vast speed it was doing. Which is not slow by any stretch of the imagination.

 

[ghwellsjr]

So someone is passing by me at ~the speed of light, which I believe would make them appear to be stationary from my point of reference. I decide to reach out and grab their hand. What happens?

As someone is approaching you at a very high speed, they will appear to you to be moving very rapidly. If you could see a clock traveling with them, you would see its hand going around very fast. If you could watch him pacing up and down in his rocket ship, you would see him running up and down extremely fast.

If you let this person pass by you, then you would immediately see all his actions and his clock slow down.

What you remember reading about was probably referring to Time Dilation where according to your rest frame, his clock and actions are going at a constant slower rate than yours the entire time, approaching, passing, and receding, but that is not something that you can observe simply by looking at him.

So knowing that all of his actions actually appear much faster than yours as you approach, are you sure you want to reach out and grab his hand? Would you even want to do this if you were both on bicycles traveling at 20 miles per hour?

 

[PeterDonis]

As someone is approaching you at a very high speed, they will appear to you to be moving very rapidly. If you could see a clock traveling with them, you would see its hand going around very fast. If you could watch him pacing up and down in his rocket ship, you would see him running up and down extremely fast.

If you let this person pass by you, then you would immediately see all his actions and his clock slow down.

This brings up an important point; here the words "appear" and "see" are being used in the literal sense--what you would actually see with your eyes looking at the light rays coming from the person/object.

In previous posts by me and others, we were using those same words to refer to something different--what you would calculate as the object's "apparent" clock rate relative to yours, after taking the light signals you actually are seeing (in the literal sense) and correcting that data for light travel time.

This is an unfortunate ambiguity in the way such scenarios are often described in ordinary language, and it's good to bring it up and make it explicit.

 

[ghwellsjr]

In previous posts by me and others, we were using those same words to refer to something different--what you would calculate as the object's "apparent" clock rate relative to yours, after taking the light signals you actually are seeing (in the literal sense) and correcting that data for light travel time.

You make it sound so easy, like you merely observe with your eyes and then do some calculations and bingo, you've got Time Dilation. But I don't think it's quite that easy. How do you know what the light travel time is by just looking?

 

[PeterDonis]

How do you know what the light travel time is by just looking?

If all you have is one single observation, obviously you don't. But if you have a whole sequence of observations, with the apparent Doppler effect changing in a certain way, you can figure out from that what the light travel times must have been--or, to put it another way, you can reconstruct the object's trajectory in the coordinates of your rest frame.

The more important point is the key conceptual distinction between what is actually observed (the Doppler-shifted light signals) and what is constructed (the object's worldline expressed in the coordinates of a particular inertial frame).

 

[ghwellsjr]

If all you have is one single observation, obviously you don't. But if you have a whole sequence of observations, with the apparent Doppler effect changing in a certain way, you can figure out from that what the light travel times must have been--or, to put it another way, you can reconstruct the object's trajectory in the coordinates of your rest frame.

No one is suggesting a single observation, I think everyone agrees that the observer has been watching the other guy constantly for a fair amount of time from some distance away as he is approaching. Must we assume that he is traveling at a constant speed and a constant direction for your scheme to work? Must we assume that he must pass right by the observer for it to work?

In any case, I think it is instructive to point out, as you did, that he can't determine the light travel times in real time, however, if all he wants to know is the Time Dilation factor, and the other guy is approaching him inertially from far away on a trajectory that will take him right by the observer, then he can instantly determine the Time Dilation factor from the Doppler, he doesn't need to know the light travel time.

 

[PeterDonis]

Must we assume that he is traveling at a constant speed and a constant direction for your scheme to work? Must we assume that he must pass right by the observer for it to work?

It depends. Generally, there are two observables that are used to determine the object's worldline: Doppler shift and transverse angular rate (i.e., the rate at which the observed direction to the object changes). The fastest determination will be made in cases where both observables are significant--i.e., where both the distance and the direction to the object are changing at significant rates that are easily detected. The most difficult cases are the limiting cases in which only one observable has significant change--purely radial motion (where you indeed might not be able to make a definite determination until the object passes right by you) and purely transverse motion.