Faster than the speed of Light ?

[Physics_Kid]

my question will be obvious when i describe this special disk in space.

a very very thin (1 carbon-12 atom thick) disk is constructed in a remote part of space, so remote there is absolutely nothing, no solar wind, no light, no gravity, nothing. the disk has a very large radius. the disk has a circumference of 186,000 miles and it's rotating (like a wheel on axle) at 1.2rps (rotations per second, or 432° per sec). is this possible? why?

just as a hint to what I'm asking, I'm interested in knowing about the edge of the disk while its rotating.

 

[JesseM]

No, in relativity this should not be possible, it would take an infinite amount of energy to accelerate any object with mass to the speed of light. In general, it's not possible to have perfectly rigid objects in relativity, any time you grab on to part of an object (the center of your disk, for example) and push or twist it, this will create a wave of deformation that travels through the object at the speed of sound in whatever material it's made of.

 

[DaveC426913]

As Jesse points out, you would not be able to accelerate the rotation high enough. You would require more & more torque to increase rotation speed as the edge of the disk approached the speed of light and began increasing in mass. At some point, you would be unable to increase the rotation speed any further no mattrer how much energy you put into it.

 

[Physics_Kid]

hmmmm, ok, let me pose another odd-ball question.

a man builds a high powered laser into a turn table. the table is extremely balanced and rotates on a frictionless bearing. the table spins at 100 rps (rotations per second). a planet far far away is a diatance away from the laser so that if this distance was the radius of a circle the circle's circumference would be 186,000 miles. a man on that planet is holding up a very large piece of untra-white oak-tag and he notices a red laser spot moving across his oak-tag. he marks two points along the laser trail so that the 2 points are 1m apart. as he looks at the paper he notices that the laser looks like a flashing red line (on, off, on, off, on, off, ...). he decides to clock how long it takes for the laser dot to move from one point to the other.

what does he measure? is the laser even a "dot" anymore at that distance and "speed" ??

 

[dicerandom]

I believe in that instance the man would measure the laser sweeping across his paper at a speed greater than c (assuming c is 186,000 miles per second, I only have it memorised in MKS and CGS). This doesn't violate relativity however as the light is made up of individual photons, each of which are traveling with an entirely radial velocity of c. The fact that a whole group of photons happen to sweep out a path that changes with some 'velocity' greater than c does not mean that the photons themselves are traveling at that speed.

 

[DaveC426913]

a] what is untra-white oak-tag?

b] Yes, superluminal movement is possible. You don't need all that gadgetry. All you need is a flashlight. Point it at Vega, then point it at Polaris. Presto - superluminal movement.

But note that, while the spot of light has moved from point A to point B, nothing tangible (not even photons) have moved faster than c. Also note that no information can be transmitted from Vega to Polaris faster than c.

In reality, what we are calling the "spot of light" is not a single discreet object, it is only semantically "the same object" because we say it is.

 

[Physics_Kid]

a] what is untra-white oak-tag?

b] Yes, superluminal movement is possible. You don't need all that gadgetry. All you need is a flashlight. Point it at Vega, then point it at Polaris. Presto - superluminal movement.

But note that, while the spot of light has moved from point A to point B, nothing tangible (not even photons) have moved faster than c. Also note that no information can be transmitted from Vega to Polaris faster than c.

In reality, what we are calling the "spot of light" is not a single discreet object, it is only semantically "the same object" because we say it is.

that should be "ultra-white oak-tag", thick paper, so the space guy can see the laser dot more easily, etc.

what about a massless item such as pure energy, can it go faster than c?

as for my example, as the laser rotates it sweeps the sky just like we see a radar tracking screen sweeps the screen while tracking aircraft. i am interested in knowing what is going on with the laser beam as function of radius (the further away from table center). if the beam were rigid (as in my 1st post) the tangental velocity would increase as the radius increased. if the beam can't be greater than c then what happens to the beam?? do the photons start to seperate?

 

[JesseM]

that should be "ultra-white oak-tag", thick paper, so the space guy can see the laser dot more easily, etc.

what about a massless item such as pure energy, can it go faster than c?

as for my example, as the laser rotates it sweeps the sky just like we see a radar tracking screen sweeps the screen while tracking aircraft. i am interested in knowing what is going on with the laser beam as function of radius (the further away from table center). if the beam were rigid (as in my 1st post) the tangental velocity would increase as the radius increased. if the beam can't be greater than c then what happens to the beam?? do the photons start to seperate?

As others have said, the spot made by a laser beam on a surface--say, the moon--can move faster than light, but if you think of the beam as being made of a train of separate photons then no individual photon is moving faster than light, it's just a series of different photons hitting the surface of the moon at different locations. No matter, energy, or information can ever move faster than light, according to relativity.

 

[DaveC426913]

what about a massless item such as pure energy, can it go faster than c?

What is light if not that?

 

[Physics_Kid]

What is light if not that?

indeed. but my ponderance of such (can pure energy go faster tha c) has no proof that it cannot. we know that the fastest thing we know of is c, and that things that have mass cannot be accelerated past c, and we have some limiting math (e=mc^2), etc, but what's hard for me to understand is why a handful of pure energy cannot go faster than c.

i guess what I'm saying is, if we knew of some other energy that went slightly faster than "c", let's says "d", would the equation then be e=md^2 ??


my days of physics have come and past (i think), and i now can only listen to what the good guys have to say, Brian Greene @ Columbia is my favorite guy, he's darn cool (smart).

 

[jtbell]

what's hard for me to understand is why a handful of pure energy cannot go faster than c.

What exactly do you mean by "pure energy?" How would I get a handful of pure energy?

 

[DaveC426913]

...what's hard for me to understand is why a handful of pure energy cannot go faster than c.

It's hard to describe briefly...

c is not simply a speed limit; it's not that something stops you from exceeding it; it's more like the concept of exceeding it is meaningless. It is part of the geometry of our space time.

Consider the question: Why can't you go farther north than the North pole? What if, when you got there, you just went a little farther? Well, it doesn't make sense to ask the question, does it? Or, at least, it doesn't make sense to try to answer it. You simply can't go farther north than the NP. There's no barrier, it's just a question of geometry isn't it?

Well, our space-time continuum is 4-dimensional.
- Time is the 4th dimension
- velocity = distance over time
- at the speed of light, time is zero, thus, velocity is undefined
- you can't go "a little faster than" undefined
(don't take all that too literally, I'm just making a point)

The speed of light is, in a sense, the 4D universe's North Pole.

 

[DaveC426913]

Another example:
- You and a friend are both sitting on a large rolling office chair (you're very good friends!).
- She wants to go due West to the coke machine, you want to go due South to the fridge.
- You push with all your might South, but she is still pushing West.

How hard do you have to push in order to head due South? Well, you'd have to push infinitely hard (no matter what you did, as long as she is pushing West, you will never be able to travel due South - you'll miss the fridge, even if only by a small amount).

So, the question is asked: what if you just pushed a little harder, could you then end up heading a little bit East?

No. The best you can hope to achieve is arbitrarily close to South (but still West). It's not a speed limit, it's geometry.

 

[JesseM]

It's hard to describe briefly...

c is not simply a speed limit; it's not that something stops you from exceeding it; it's more like the concept of exceeding it is meaningless. It is part of the geometry of our space time.

Consider the question: Why can't you go farther north than the North pole? What if, when you got there, you just went a little farther? Well, it doesn't make sense to ask the question, does it? Or, at least, it doesn't make sense to try to answer it. You simply can't go farther north than the NP. There's no barrier, it's just a question of geometry isn't it?

Well, our space-time continuum is 4-dimensional.
- Time is the 4th dimension
- velocity = distance over time
- at the speed of light, time is zero, thus, velocity is undefined
- you can't go "a little faster than" undefined
(don't take all that too literally, I'm just making a point)

The speed of light is, in a sense, the 4D universe's North Pole.

I don't think the analogy with the north pole really works, because relativity does in principle allow for the existence of tachyons, which always travel faster than c.

 

[DaveC426913]

I don't think the analogy with the north pole really works, because relativity does in principle allow for the existence of tachyons, which always travel faster than c.

Of course it's not a perfect analogy! It's just a conceptualizing thing to hopefully help the OP understand why c is not simply an arbitrary barrier.

(BTW, while faster than c particles are not explicitly forbidden, tachyons can't slow down to c. Thus, c, as a barrier, can never be crossed - either way.)

 

[Physics_Kid]

Of course it's not a perfect analogy! It's just a conceptualizing thing to hopefully help the OP understand why c is not simply an arbitrary barrier.

(BTW, while faster than c particles are not explicitly forbidden, tachyons can't slow down to c. Thus, c, as a barrier, can never be crossed - either way.)

i know this is not the correct comparison, but they had the same problem with aircraft going faster than sound...

i understand the physics/math have a strong backing for c being a speacial quantum thing, but the universe is a big unknown place. how many parallel universes are there? is there life elsewhere in a closeby galaxy? possibilities exist, and with a universe that is infinitely big that possibility must be true somewhere.

 

[JesseM]

i know this is not the correct comparison, but they had the same problem with aircraft going faster than sound...

It's not correct because no one ever believed the laws of physics insured this was absolutely impossible, they just thought it could never be done as a practical matter. Also, the speed of sound is not built into basic equations of physics in the way the speed of light is. For example, a clock that is moving at velocity v relative to you will be observed to slow down by a factor of $$\sqrt{1 - v^2/c^2}$$, and this formula has been experimentally tested in many ways, like observing how the decay time of certain particles gets longer as their speed is increased, or the way that this slowdown is incorporated into the GPS satellite system. Another such formula is the one for the energy of a moving object whose rest mass is m, $$E^2 = m^2 c^4 + p^2 c^2$$, where p is the relativistic momentum, $$p = mv / \sqrt{1 - v^2/c^2}$$. If m is nonzero, then the energy would become infinite at v=c, according to this formula.