Can Propeller Speeds and Wave Breaks Challenge the Speed of Light?

[PRH]

TL;DR Summary

Two questions to get more insight into general relativity

Hi, I have two topics:

1) Suppose a propeller is spinning very fast (say it's in a vacuum, no drag) and we arbitrarily lengthen its blades. Eventually the velocity of the tips of the propeller will approach the speed of light. That should be a speed limit, but that implies that the blades of the propeller will deform, probably into a spiral shape, with the pitch of the spiral becoming greater with time. How to think about this?

2) We're at the ocean on a very long, straight beach. A wave approaches the beach at a slight angle, and the 'break' of the wave moves rapidly along the length of the beach. Increase the velocity of the wave and reduce its angle relative to the shore and eventually the break of the wave should be traveling faster than the speed of light. But the water molecules at the crest are not actually moving along the beach so rapidly. How to think about this in the context of relativity?

Thanks!

 

[Dale]

TL;DR Summary: Two questions to get more insight into general relativity

1) Suppose a propeller is spinning very fast (say it's in a vacuum, no drag) and we arbitrarily lengthen its blades. Eventually the velocity of the tips of the propeller will approach the speed of light. That should be a speed limit, but that implies that the blades of the propeller will deform, probably into a spiral shape, with the pitch of the spiral becoming greater with time. How to think about this?

It will deform long before that. It will deform so much that it breaks apart roughly when the tangential velocity of the ends approaches the speed of sound in the material. That is far less than the speed of light.

TL;DR Summary: Two questions to get more insight into general relativity

2) We're at the ocean on a very long, straight beach. A wave approaches the beach at a slight angle, and the 'break' of the wave moves rapidly along the length of the beach. Increase the velocity of the wave and reduce its angle relative to the shore and eventually the break of the wave should be traveling faster than the speed of light. But the water molecules at the crest are not actually moving along the beach so rapidly. How to think about this in the context of relativity?

Nothing in relativity forbids that.

 

[Doc Al]

TL;DR Summary: Two questions to get more insight into general relativity

2) We're at the ocean on a very long, straight beach. A wave approaches the beach at a slight angle, and the 'break' of the wave moves rapidly along the length of the beach. Increase the velocity of the wave and reduce its angle relative to the shore and eventually the break of the wave should be traveling faster than the speed of light. But the water molecules at the crest are not actually moving along the beach so rapidly. How to think about this in the context of relativity?

Plenty of "things" (that aren't really things) can go faster than light. There's the classic of shining a laser pointer at the moon. You can sweep the pointer across in a fraction of a second, but the light hitting the moon's surface will appear to move faster than light speed. And look up "superluminal scissors", similar to your example.

 

[PeroK]

... You can create the appearence of motion by having a row of lights go on in sequence. This appears like a signal is moving along the row. Whereas, in fact, the lights may be illuminating independently and there is no motion in any physical sense. Like the laser pointer, this apparent motion can have any speed. In fact, if you illuminate all the lights simultaneously, then one interpretation would be a signal of infinite speed - although it's not clear in which direction the signal moved!

 

[PRH]

Thanks for "not really a thing" and the scissors topic. So what I was describing is called 'phase velocity' and can exceed the speed of light. And the example of twitching a laser dot across the surface of the moon at greater than light speed might suggest that we can transfer information at greater than light speed, but the rub is that the laser itself would have to move at greater than light speed, right?

 

[Doc Al]

And the example of twitching a laser dot across the surface of the moon at greater than light speed might suggest that we can transfer information at greater than light speed, but the rub is that the laser itself would have to move at greater than light speed, right?

That moving laser dot cannot transfer information across the moon!

Similarly, the flashing lights (in the example from @PeroK) carry no information as they "move" along.

 

[PRH]

DocAI, I was imagining that there was an instrument sitting on the moon that detects flashes of laser light, like blips of Morse code. But for the information to flow faster than light, the laser itself, back on Earth, would need to be physically twitched back and forth faster than light, which is impossible. Does that make sense?

 

[Doc Al]

DocAI, I was imagining that there was an instrument sitting on the moon that detects flashes of laser light, like blips of Morse code. But for the information to flow faster than light, the laser itself, back on Earth, would need to be physically twitched back and forth faster than light, which is impossible. Does that make sense?

You're talking about communicating between Earth and Moon, not from one side of the moon to the other. Since you're using a light beam, all signals will be at the speed of light. (Of course! )

 

[PeroK]

DocAI, I was imagining that there was an instrument sitting on the moon that detects flashes of laser light, like blips of Morse code. But for the information to flow faster than light, the laser itself, back on Earth, would need to be physically twitched back and forth faster than light, which is impossible. Does that make sense?

The information in the laser example originates on Earth. Consider the same information sent in opposite directions and received simultaneously by two receivers a large distance apart. There is no information sent between the receivers. There is no faster than light signal.

 

[PRH]

DocAI, I was thinking that the instrument on the moon gets the information as a series of light 'pulses' from when the laser flashes over the instrument. For those flashes to communicate information faster than the speed of light, the physical direction of the laser on Earth would need to varied at greater than the speed of light.

 

[Orodruin]

DocAI, I was thinking that the instrument on the moon gets the information as a series of light 'pulses' from when the laser flashes over the instrument. For those flashes to communicate information faster than the speed of light, the physical direction of the laser on Earth would need to varied at greater than the speed of light.

No, you have completely the wrong idea here. The laser dot on the Moon’s surface will move faster than the speed of light - but it is not a physical thing moving. It is the illumination of the Moon’s surface by a series of independent light pulses from the Earth snd the sense of the dot moving is created by different arrival times. This is all created by simply and relatively slowly rotating the laser back on Earth. Nothing is actually moving faster than light. In particular the laser is not. The only information transfer is from the Earth to the Moon at lightspeed. No information is carried by the dot itself.

 

[Doc Al]

DocAI, I was thinking that the instrument on the moon gets the information as a series of light 'pulses' from when the laser flashes over the instrument. For those flashes to communicate information faster than the speed of light, the physical direction of the laser on Earth would need to varied at greater than the speed of light.

I think you're mixing things up. Imagine two people on the moon, one on each side. You can send signals to each however you want, but those signals move at the speed of light. Those two people cannot use your signal to transfer information to each other. (No matter how you move the laser, you won't be communicating faster than light.)

 

[Nugatory]

the physical direction of the laser on Earth would need to varied at greater than the speed of light.

Even if the laser could do that, there would be no faster than light information transfer to the moon. Any change in the direction the laser is pointing on earth will not be seen on the moon until light from the laser has moved from earth to moon, and that light is of course moving at the speed of light.

 

[obtronix]

TL;DR Summary: Two questions to get more insight into general relativity

1. There's no such thing as a rigid object think of the propellers as more slinky like at high speeds.

2. No information is being transferred at the speed of light. It's just an illusion of faster than light speed.