A few questions about light and relativistic effects

[coktail]

Here's a few smattered questions I've had a hard time finding good answers for:

1. Why is the speed of light a constant? Is it related to the fact that it is massless? Is it because it isn't subject to time dilation?

2. Why is the speed of sound, or EVERYTHING for that matter, not constant? For example, if you throw a ball at me, and I measure it at 5mph, and then you throw it at me again while I'm moving towards you, why do I not still measure it at 5mp due to time dilation and length contraction, just like I would light?

3. This one may be a blunder, but I have to ask: Is the speed of light really constant, or is it just that we always measure it at the same velocity due to relativistic effects? Is there any difference between these two things?

Thank you!

 

[PAllen]

Here's a few smattered questions I've had a hard time finding good answers for:

* Why is the speed of light a constant? Is it related to the fact that it is massless? Is it because it isn't subject to time dilation?

* Why is the speed of sound, or EVERYTHING for that matter, not constant? For example, if you throw a ball at me, and I measure it at 5mph, and then you throw it at me again while I'm moving towards you, why do I not still measure it at 5mp due to time dilation and length contraction, just like I would light?

* I know this one is just a blunder, but I have to ask: Is the speed of light really constant, or is it just that we always measure it at the same velocity due to relativistic effects. Is there any difference between these two things? (I hate that I just asked that)

Thank you!

1) Within special relativity, any massless particle must travel at a fixed, frame invariant speed we call c. Why special relativity is true is not a question answerable by science. As to why light travels at c, classically this follows from Maxwell's equations (but why is light described by them - who knows? In quantum theory, why is what we call light described by a massless boson (thus must travel at c)? Who knows?

2) There is one law for addition of velocities in special relativity. It covers your ball scenario as well as light: (u + v)/(1 + u*v/c^2). It happens that if u and v are much smaller than c, this is indistinguishable from u+v. If you let v=c, you will see that this yields c. So there is only one law that incorporates c as the unique, invariant, maximum speed.

3) This is not a dumb question. According to some philosophic positions, the two alternatives you propose are considered irrelevant to distinguish. However, others would say the difference is possibly meaningful, even if unobservable. On that score, there are, indeed, interpretations equivalent in all predictions to special relativity, that posit the light moves at different speed in different frames, but length contraction and time dilation conspire to make it undetectable.

 

[coktail]

Thank you so much for your reply.

As to #2, is this saying that, yes, my measurement of the ball's velocity would be affected by relativistic effects as I move towards it, but nowhere near the degree to which measurements of light are affected, and that all of that is accounted for in the singular law for addition of velocities in special relativity?

In other words, measurements of objects with mass are subject to relativistic effects just like massless objects are, but the velocity of massless objects always appears constant to us independent of our reference frame. Correct?

Sound, for example, may have a travel at a constant velocity in a perfectly uniform gas, but that velocity is NOT frame invariant. Correct?

 

[TheEtherWind]

1) No one has proven the speed of light to be constant. Hence as to why it is one of Einstein's postulates... or assumptions. However, the natural consequences that would arise from it being constant tend to be what we observe.

 

[PAllen]

1) No one has proven the speed of light to be constant. Hence as to why it is one of Einstein's postulates... or assumptions. However, the natural consequences that would arise from it being constant tend to be what we observe.

The two way speed of light being constant and frame invariant has been established to very high precision. It is the one way speed is declared to be constant by convention rather than unambiguous measurement.

 

[PAllen]

Thank you so much for your reply.

As to #2, is this saying that, yes, my measurement of the ball's velocity would be affected by relativistic effects as I move towards it, but nowhere near the degree to which measurements of light are affected, and that all of that is accounted for in the singular law for addition of velocities in special relativity?

Yes.

In other words, measurements of objects with mass are subject to relativistic effects just like massless objects are, but the velocity of massless objects always appears constant to us independent of our reference frame. Correct?

Yes.

Sound, for example, may have a travel at a constant velocity in a perfectly uniform gas, but that velocity is NOT frame invariant. Correct?

Sound is a different case, in that it is a compression wave, not a simple kinematic speed. However, it is certainly true that the speed of sound is not frame invariant.

 

[coktail]

Awesome. Thanks again!

 

[TheEtherWind]

The two way speed of light being constant and frame invariant has been established to very high precision. It is the one way speed is declared to be constant by convention rather than unambiguous measurement.

Well I suppose I disagree with the idea that the speed of light can be 'proven' like it's a mathematical theorem of some sort. Sure experiments can measure to high precision, but it is after all an anomaly of our universe. I guess I show a bit of apathy towards the 'proof' of it considering there's been no reason to further investigate it... seeing as how time dilation, gravitational dilation, etc. hasn't failed us yet.

 

[PAllen]

Well I suppose I disagree with the idea that the speed of light can be 'proven' like it's a mathematical theorem of some sort. Sure experiments can measure to high precision, but it is after all an anomaly of our universe. I guess I show a bit of apathy towards the 'proof' of it considering there's been no reason to further investigate it... seeing as how time dilation, gravitational dilation, etc. hasn't failed us yet.

I was talking about measurement, not proof. You can measure two way speed with high accuracy, and you can measure that it is not affected by motion of source or receiver. Meanwhile, constancy of one way speed of light cannot be measured unambiguously at all (no experiment can rule out certain theories in which the one way speed is anisotropic, while preserving isotropy of two way speed; many attempts at measuring one way speed don't even constitute measurements - they are true by construction).

I make this distinction because what Einstein stipulated as a convention was constancy of one way speed of light, because of the impossibility of not setting it by convention.

 

[coktail]

I'm resurrecting an old thread here to ask a new question. PAllen graciously explained the following to me:

1) There is one law for addition of velocities in special relativity. It covers your ball scenario as well as light: (u + v)/(1 + u*v/c^2). It happens that if u and v are much smaller than c, this is indistinguishable from u+v. If you let v=c, you will see that this yields c. So there is only one law that incorporates c as the unique, invariant, maximum speed.

This seems to say that the speed at which a thing is traveling affects the degree to which its measured speed is affected by relativistic effects, but how can a thing's speed affect the measurement of its speed? Isn't this circular logic? I'm sure it's not, but I love would love some help understanding where I'm going wrong here in my thinking.

As always, thank you!

 

[Agerhell]

Here's a few smattered questions I've had a hard time finding good answers for:

1. Why is the speed of light a constant? Is it related to the fact that it is massless? Is it because it isn't subject to time dilation?

You of course have the well known Shapiro Delay. Light slows down in a gravitational field, noticed for instance when sending signals to a space probe and the signal passes near Jupiter. However,as a clock will slow down by exactly the same amount in a gravitational field, locally the speed of light will appear constant.

 

[PAllen]

I'm resurrecting an old thread here to ask a new question. PAllen graciously explained the following to me:



This seems to say that the speed at which a thing is traveling affects the degree to which its measured speed is affected by relativistic effects, but how can a thing's speed affect the measurement of its speed? Isn't this circular logic? I'm sure it's not, but I love would love some help understanding where I'm going wrong here in my thinking.

As always, thank you!

I'm not understanding your conundrum. If I measure the speed of two things, I just have two speeds measured independently. Velocity addition formula comes into play when:

I measure you going u, you measure Jane going v, and tell me this. The I find that when I measure Jane's speed I get (u+v)/(1+uv/c^2).

or:

I measure going u, and Jane going v (in the same direction, slower). Instead of u-v, you report that you measure Jane going (u-v)/(1-uv/c^2).

I don't see anything circular here. The formula relates measurement by one observer, to measurement by a different observer, based on the relative motion of the two observers.

 

[PAllen]

You of course have the well known Shapiro Delay. Light slows down in a gravitational field, noticed for instance when sending signals to a space probe and the signal passes near Jupiter. However,as a clock will slow down by exactly the same amount in a gravitational field, locally the speed of light will appear constant.

Let's not bring GR into this. OP is still trying to understand SR. Further, one can debate, in GR, whose statement is real versus appear? Why claim light only 'appears' to move at c locally? This seems to prefer one class of coordinates/observers over others.

 

[coktail]

Ok, let's say you and I are facing each other. You have a flashlight in one hand, and a ball in the other. You turn on the flashlight and throw the ball, and I measure the speed of both. For the ball, I get a measurement of 10mph. For the light, I get c.

Now we repeat the experiment while I am walking towards you at 5mph. This time I measure the ball at 15mph, but the light is still c.

From previous posts, I have gathered that relativistic effects are occurring between myself and both the ball and the light, but that because the ball is moving at an insignificant fraction of c, the relativistic effects are so minute that they are practically negligible. There is one equation describes the relativistic effects that occur for both the ball and the light.

The faster I am moving relative to something, the less its velocity changes along with changes in my FoR (due to relativistic effects kicking in), and once you reach the speed of light, velocity becomes altogether unaffected by FoR.

However, and this is that part that has me confounded, how can object's speed affect the degree to which it is affected by relativistic effects when relativistic effects affect our measurements of an object's speed.

As an aside, I know that I am arguable putting the cart before the horse by attributing the invariance of c to relativistic effects, but things make more sense to me when I think of them that way.

Again, I'm not setting out to poke holes in relativity, but just to understand how/why I'm thinking about this particular aspect if incorrectly.

I hope this clarifies. Thanks.

 

[Nugatory]

However, and this is that part that has me confounded, how can object's speed affect the degree to which it is affected by relativistic effects when relativistic effects affect our measurements of an object's speed.

The ball has whatever speed it has relative to you, you can measure that speed, and you're done, no problem.

You're confusing yourself by thinking that the ball's speed relative to me has anything to do with what you see in this thought experiment... Sure, you're walking towards me at 5 mph, but that has nothing to do with you and the ball... Imagine that we're doing the thought experiment in empty space, just you, me, and the ball. And after I throw the ball, I disappear. Now there's just you and the ball, no 5mph relative to anything, nothing to compare the speed of the ball against except you.

 

[PAllen]

Ok, let's say you and I are facing each other. You have a flashlight in one hand, and a ball in the other. You turn on the flashlight and throw the ball, and I measure the speed of both. For the ball, I get a measurement of 10mph. For the light, I get c.

Now we repeat the experiment while I am walking towards you at 5mph. This time I measure the ball at 15mph, but the light is still c.

From previous posts, I have gathered that relativistic effects are occurring between myself and both the ball and the light, but that because the ball is moving at an insignificant fraction of c, the relativistic effects are so minute that they are practically negligible. There is one equation describes the relativistic effects that occur for both the ball and the light.

The faster I am moving relative to something, the less its velocity changes along with changes in my FoR (due to relativistic effects kicking in), and once you reach the speed of light, velocity becomes altogether unaffected by FoR.

However, and this is that part that has me confounded, how can object's speed affect the degree to which it is affected by relativistic effects when relativistic effects affect our measurements of an object's speed.

As an aside, I know that I am arguable putting the cart before the horse by attributing the invariance of c to relativistic effects, but things make more sense to me when I think of them that way.

Again, I'm not setting out to poke holes in relativity, but just to understand how/why I'm thinking about this particular aspect if incorrectly.

I hope this clarifies. Thanks.

It doesn't clarify your concern at all. There is one formula, applying exactly, to all cases. If you don't like that formula, sorry, the world didn't ask your permission. The same formula that says:

If you drop a reference object, then move away from it at the same speed you saw me approaching, then measure my speed: if we are doing this at 20 mph, you see 40-epsilon mph after; also says if we are doing this .9c you see me at .9945 c after.

I can't attach any conceivable meaning to this statement:

"how can object's speed affect the degree to which it is affected by relativistic effects when relativistic effects affect our measurements of an object's speed. "

I'm always at rest relative to myself. My measurements have no relativistic affects on them. Relativistic effects apply to what I measure about things moving fast relative to me. This goes for every observer.

 

[Apophenia]

1) Within special relativity, any massless particle must travel at a fixed, frame invariant speed we call c. Why special relativity is true is not a question answerable by science. As to why light travels at c, classically this follows from Maxwell's equations (but why is light described by them - who knows? In quantum theory, why is what we call light described by a massless boson (thus must travel at c)? Who knows?

2) There is one law for addition of velocities in special relativity. It covers your ball scenario as well as light: (u + v)/(1 + u*v/c^2). It happens that if u and v are much smaller than c, this is indistinguishable from u+v. If you let v=c, you will see that this yields c. So there is only one law that incorporates c as the unique, invariant, maximum speed.

3) This is not a dumb question. According to some philosophic positions, the two alternatives you propose are considered irrelevant to distinguish. However, others would say the difference is possibly meaningful, even if unobservable. On that score, there are, indeed, interpretations equivalent in all predictions to special relativity, that posit the light moves at different speed in different frames, but length contraction and time dilation conspire to make it undetectable.

1) What evidence is there that light is actually massless? Was the boson predicted in retrospect to the assumption that light was massless?

 

[PAllen]

1) What evidence is there that light is actually massless? Was the boson predicted in retrospect to the assumption that light was massless?

See our own FAQ:

https://www.physicsforums.com/showthread.php?t=534862

The last reference answers your question.

 

[Agerhell]

Let's not bring GR into this. OP is still trying to understand SR. Further, one can debate, in GR, whose statement is real versus appear? Why claim light only 'appears' to move at c locally? This seems to prefer one class of coordinates/observers over others.

? If you are sending some kind of spacecraft out in the solar system and you want to correctly calculate the time it will take to send signals from the Earth and to that spacecraft and you know that the signal will pass near Jupiter you will have to take the fact that light will slow down near Jupiter into account. I do not quite understand where you are going with this.

 

[PAllen]

? If you are sending some kind of spacecraft out in the solar system and you want to correctly calculate the time it will take to send signals from the Earth and to that spacecraft and you know that the signal will pass near Jupiter you will have to take the fact that light will slow down near Jupiter into account. I do not quite understand where you are going with this.

I'm just objecting to characterizing one local observers direct measurements as 'appear' versus another's without using this pejorative. As for 'light slowing down near Jupiter', it encompasses nothing more than a very convenient coordinate choice. There is no invariant meaning attached to it. If you want to discuss this further, please start a new thread, but in GR, speed of light at a distance from you is inherently a purely conventional quantity.

 

[coktail]

One more question/clarification to add on here. Let's go back to my original thought experiment, but add a ball moving at .9c. So now the experiment looks like this:

You have a flashlight in one hand, and two balls in the other (ball A and ball B). You turn on the flashlight and throw the first and second ball, and I measure the speed of all three. For ball A I get a measurement of 10mph, for ball B I get a measurement of .9c (you've got a great pitching arm), and for the for the light I get c.

Now we repeat the experiment while I am walking towards you at 5mph. This time I measure ball A at 15mph, and the light is still c, but what is my measured speed of ball B? Would it be something less than .9c + 5mph because its speed is a significant enough fraction of c that you'd have to take into account the relativistic addition of velocities?

 

[PAllen]

One more question/clarification to add on here. Let's go back to my original thought experiment, but add a ball moving at .9c. So now the experiment looks like this:

You have a flashlight in one hand, and two balls in the other (ball A and ball B). You turn on the flashlight and throw the first and second ball, and I measure the speed of all three. For ball A I get a measurement of 10mph, for ball B I get a measurement of .9c (you've got a great pitching arm), and for the for the light I get c.

Now we repeat the experiment while I am walking towards you at 5mph. This time I measure ball A at 15mph, and the light is still c, but what is my measured speed of ball B? Would it be something less than .9c + 5mph because its speed is a significant enough fraction of c that you'd have to take into account the relativistic addition of velocities?

You just use the same formula for all cases, all objects. If you have sufficient precision, there are relativistic effects at walking speed (recent experiments with latest generation atomic clocks have shown relatavistic effects at speeds like 10 mph, as well as gravitational effects at a couple of feet change in altitude).

So, your answers would be 15 mph (to any possible precision), .9c + 1 mph (approx.), and c.

The approximation I used is simply: (.9 + ε)/(1+.9ε) ≈ .9 + ε - .81 ε
ignoring any terms in ε^2.

 

[coktail]

Thank you!