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Today's Physics Question....?

#21
Lonesomedave said:
while it's quite true to say i have not grasped the concept of relativity, i think you missed my point.

some of these guys were saying that the light emitted by the emitter would never reach the receiver because the combined speeds were, in effect, 6/4 the speed of light.

i was trying to say that is not true. the speed of light is fixed, and as soon as it is emitted, it starts chasing (at c) an object whose velocity is 3/4 c....so it will catch up

davesignatureII-1.png
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I get you now. I guess I was thinking like a physicist (I'm not one) and I thought you meant the two objects had a speed of 3/4 c relative to each other.

The reasons you have a conundrum is that you think have set the relative speed of the two objects at 6/4 c. This can't happen. The fastest any two objects can move apart relative to one another is c.

It is possible for an observer (you) to look in one direction and see an onject travelling away at 3/4c, and then turn round and see an object travelling the opposite way at the same speed. But second or third observer travelling on either object would measure their relative speed as c or less. Such an observer could never record a result of greater than c.
 
#22
Lonesomedave said:
ok...so today i am asking about the red shift of light

suppose you have two objects in space, right next to each other (although, i suppose, it really doesn't matter what the initial state is)

suppose they start moving directly away from each other at 3/4 (75%) of light speed. that is, each one is moving at 3/4 light speed

suppose one emits a beam of light that ultimately catches up with the other

how much would the light be red shifted and what would determine the red shift?

i believe it would be determined by both their speeds. here is my thinking: since, as i understand it, red shift is caused by the fact that light emitted from a moving object will have the peaks and troughs of it waves emitted at a slightly greater distance from each other than a stationary object

therefore, shouldn't the receiving object's speed cause the light waves to be received at a slightly greater distance from each other than if the object were stationary?

Bill, Mohawk, Titus, any physics or astronomy guys out there...put on your thinking caps

davesignatureII-1.png
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To break it down, let's say the speed of light is 100 MPH. If you had two people moving away from each other at 75 MPH in space where there is no wind resistance. Then, one person throws a ball at 100 MPH to the other person, it will never reach the other person unless the ball was thrown at a point where it had a chance to catch up. After an hour, both persons would be 150 miles apart so we know in that case, the question is moot. But if the two persons were closer such that the ball could catch up to the other person, then if the ball was light moving at the speed of light, "red shift" would occur for the person receiving the light beam.
 
#23
Nope, you're right Dave. I missed that too.

Placedesjardins, in your example it would hit the person eventually. From the point the ball was thrown it would be traveling 100 miles in one direction (giving the ball the same characteristics of light).

My apologies for questioning it.
 
#24
Lonesomedave said:
yeah, i used to think that too...but unless these guys have taught me wrong, it is not true.

the speed of light is c (@ 186,000 miles per second) and it does not care what the speed of it's emitter is

thus, when the emitting object emits the light, it goes out at c and it is chasing an object that is only moving at 3/4 c, so it WILL catch up

davesignatureII-1.png
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You're right, and I should have known better than to do a quick read and then type out a hasty reply without thinking. :hiding:
 
#28
There cannot be something moving at 150% the speed of light. Assuming that these objects go at 0.75c away from each other (224844.343500km/s), their relative speed is 287,800.75968 km/s. I remember that much from school. I assume that we can just treat this as firing a light beam from an object moving ~287800km/s away
 
#29
bassybill said:
Interesting - I've never seen that convention. Is it an old, obsolete thing? The international symbol for the speed of light is lower case c.

http://physics.info/constants/
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Perfect. Just perfect. Everywhere I look, they use the same 'c' for both.

Might just explain how/why the Mars Lander came in a bit, shall we say "hot". If the international scientific community can't keep their units and symbols straight....

I know, they'll say "Well, you should know what the formula is used for, by the other details.

I call shenanigans!
 
#31
bassybill said:
You still haven't grasped the idea of relativity, Dave. That's unsurprising as it's a tricky concept.

It's meaningless to think of the light going one way and the emitter moving the other. As soon as a pulse of light is emitted, the photons of light and the emitter get further apart at the rate of c. That's it. That's all you can say. It's doesn't mean anything to talk of the emitter moving in the opposite direction as there's no such thing as absolute motion.
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You're using an omnidirectional light source, when it could be a laser which isn't absolutely focused well enough to eliminate scatter, but it works well enough over fairly long distances. If that's the case, the emitter and light pulse (or, beam) could definitely be moving in opposite directions, right?
 
#32
hbarcat said:
You are describing a situation that can't happen. Their combined velocity causes then to separate at a speed greater than the speed of light, (1.5 x C) and therefore any light beam emitted by either will never reach the other.
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They are moving apart from each other at 1.5 C but that doesn't mean the light cannot catch up with the object which isn't emitting.

Two objects, A and B, are travelling away from each other at 75% speed of light, after 10 minutes, they are both 7.5 light minutes away from the start point and 15 light minutes away from each other. At this point object A begins emitting light.

Let's put this on a 1D axis of distance, imagine 0 is the start point, A is currently at +7.5 light minutes and B is currently at -7.5 light minutes. At this point a photon - P is launched from A towards B. While A is still moving in the + direction at 75% the speed of light, the photon doesn't maintain the momentum which A had, so it is now moving towards B at 100% the speed of light, while B is only moving at 75%.

10 minutes : A=+7.5 B=-7.5 P=+7.5
20 minutes : A=+15 B=-15 P=-2.5
30 minutes : A=+22.5 B=-22.5 P=-12.5
40 minutes : A=+30 B=-30 P=-22.5
50 minutes : A=+37.5 B=-37.5 P=-32.5
60 minutes : A=+45 B=-45 P=-42.5
70 minutes : A=+52.5 B=-52.5 P=-52.5

So while the relative speeds may indeed be greater than the speed of light, the 75% C of the object emitting the light is irrelevant to the speed of any emitted light.

Though I'm probably talking gibberish. Re-red shift, ich! Will look in the morning :p
 
#33
Bocete said:
There cannot be something moving at 150% the speed of light. Assuming that these objects go at 0.75c away from each other (224844.343500km/s), their relative speed is 287,800.75968 km/s. I remember that much from school. I assume that we can just treat this as firing a light beam from an object moving ~287800km/s away
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One object can't move that fast, but the speed of two objects moving in opposite directions (acknowledging that they couldn't be small enough to bypass each other at any point AND be co-linear, so it can't accurately be considered their 'velocity' but assuming it's close enough for the explanation) is additive and the point is, they're moving at 1.5 times the speed of light relative to each other.
 
#34
1958Bassman said:
You're using an omnidirectional light source, when it could be a laser which isn't absolutely focused well enough to eliminate scatter, but it works well enough over fairly long distances. If that's the case, the emitter and light pulse (or, beam) could definitely be moving in opposite directions, right?
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The emitter will be, but the light will not keep the momentum of the source.

Also, physics side note, there will still be scatter. Scatter is what happens when light interacts with *stuff*, even a perfectly collimated beam would suffer scattering effects. Divergence is what you want to avoid (focusing would also be an issue, as beyond a focal point the beam will diverge). Collimation is where the photons are parallel along the beam path.
 
#35
1958Bassman said:
One object can't move that fast, but the speed of two objects moving in opposite directions (acknowledging that they couldn't be small enough to bypass each other at any point AND be co-linear, so it can't accurately be considered their 'velocity' but assuming it's close enough for the explanation) is additive and the point is, they're moving at 1.5 times the speed of light relative to each other.
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Pretty sure that's not how special relativity works. By special relativity, if two lightbeams are moving away from eachother, in the same line and in vacuum and all that, they are getting away from eachother at the speed of light. That is, either beam is moving at the speed of light if we were to measure from the relative perspective of the other beam.

The numbers I gave correspond to this. Either beam is moving at 0.75c from a common point, so from the perspective of either beam, the other beam is moving away at about 0.96c. This is significantly faster than the speed at which the common point is getting away, but still less than 1c. To get to 1c both beams would need to accelerate to 1c.

It's weird and so fun. I in no way understand all of this, but speeds to 'bend' to be below 1c as you change the perspective, and in case of actual light beams in vacuum, things get sooooo unintuitive.
 
#36
1958Bassman said:
One object can't move that fast, but the speed of two objects moving in opposite directions (acknowledging that they couldn't be small enough to bypass each other at any point AND be co-linear, so it can't accurately be considered their 'velocity' but assuming it's close enough for the explanation) is additive and the point is, they're moving at 1.5 times the speed of light relative to each other.
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See fdeck's post about the special relativity velocity addition formula. They are not moving at 1.5 times the speed of light relative to each other - they can't. Yes, I know it's counterintuitive.

Their relative velocity would be 0.96c according to this calculator.

http://www.orionsarm.com/fm_store/RTTCalc.htm
 
#37
Avoiding the maths, it's also worth considering the Cosmic Microwave Background Radiation.

This is evidence of the wavelength of photons from the most distant reaches of the universe being 'stretched' by the Doppler Effect way beyond red-shift, through infra-red and into microwave.

I think some of the confusion arises from not being clear about where any proposed measurements c would be taken from.

As an external observer, it would seem that if two galaxies receded from each other at a relative speed >c, then yes, there's your 'faster than light' argument. But despite the maths saying this is intuitively possible - in fact it does happen at much slower speeds - at light speed that maths doesn't work. You need to consider the Lorentz factor and the idea of inertial frames of reference.

In order to determine their relative speeds, you'd have to travel within one of the galaxies. Even then, you wouldn't be able to record the movement of a photon from any point A to any point B and arrive at a result >c.

Another thing worth thinking about that begins to link special relativity (the subject of this thread) with the much more gruelling general relativity, is this:

According to special relativity, as speeds approach c, mass approaches infinity. If, then, if we are moving away from other galaxies at speeds approaching c, why don't we 'feel' that extra gain in mass?
 

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