Light velocity paradox

TheMadFool

The great Albert Einstein postulated that the velocity of light is constant at approximately 300,000 km/s. This one postulate and maybe a few more is the allegedly the foundation of his theory of relativity, a theory that has withstood many attempts at disproof. So far so good.

An essential component of moving objects is relative velocity i.e. the difference between the velocities of objects moving with respect to each other.

Consider 2 cars, A and B, moving on the same practically straight freeway.

1. Situation 1: A is moving at 20 km/h north and B is moving 60 km/h north. The relative velocity of B with respect to A is 60 - 20 = 40 km/h.

2. Situation 2. Imagine A moving at 20 km/h south and B is moving 60 km/h north. Then the relative velocity of B with respect to A is 60 - (-20) = 60 + 20 = 80 km/h

Suppose now that we wish to maintain the relative velocity at one value but increase the velocity of A in situation 1 to 30 km/h. To ensure we get the same relative velocity, we must increase the velocity of B proportionately to 70 km/h so that 70 - 30 = 40 km/h (the desired relative velocity remaining constant)

On the other hand in situation 2, if we wish to maintain the same relative velocity of 80 km/h then if we increase the speed of A to 30 km/h from 20 km/h then we must decrease the velocity of B to 50 km/h which gives us 50 - (-30) = 50 + 30 = 80 km/h (the desired relative velocity remaining constant)

In other words, to maintain the same relative velocity between two objects, changes in the velocity of one object must be compensated with a change in the velocity of the other object.

What then of the postulate that the relative velocity of light with respect to an object is "constant"? If I'm travelling in a spaceship with a given velocity, the relative velocity of light with respect to my spaceship will be 300,000 km/s. If I were then to alter my velocity, doesn't the velocity of light have to change accordingly so as to ensure that the relative velocity stays at a constant 300,000 km/h?

What gives?

Metaphysician Undercover

What then of the postulate that the relative velocity of light with respect to an object is "constant"? If I'm travelling in a spaceship with a given velocity, the relative velocity of light with respect to my spaceship will be 300,000 km/h. If I were then to alter my velocity, doesn't the velocity of light have to change accordingly so as to ensure that the relative velocity stays at a constant 300,000 km/h?

What gives? — TheMadFool

Einstein's special relativity produces consistency between the premise that all motions are relative, as you describe, and the premise that the velocity of light is always the same. So, according to special relativity, all velocities are relative as you describe, except the velocity of light which is constant, (absolute, you might say). Then the theory puts forward principles for dealing with these (somewhat contradictory) premises.

TheMadFool

↪Metaphysician Undercover

Ok. Thanks.

Gnomon

What then of the postulate that the relative velocity of light with respect to an object is "constant"? — TheMadFool

I don't fully understand how this works technically. But, metaphorically, I assume that Einstein realized that everything in space-time must be moving & changing relative to something infinite-eternal. Some astrologers viewed God or the Sun as the Eternal center about which everything else revolves. So, Einstein chose the speed of light, measured relative to Earthlings, to set as a mathematical constant to which other things can be compared. I don't know if he was thinking of the Sun analogy, but it makes a nice metaphor. :nerd:

Note : Physical "constants" are sometimes measured, but Mathematical constants are sometimes created by definition, to serve as an Axiom. Einstein's Cosmic Constant was an example of the latter. But it was eventually found to have a physical basis.

TheMadFool

↪Gnomon

Ok. Thanks.

Pfhorrest

↪TheMadFool

The short version is that observers in different states of motion will observer both space and time to be distorted relative to each other such that no matter anyone's state of motion, they will always observe light to traverse the same space in the same time. The consequence of this is that other things besides light appear expanded or contracted in space or time: observers will see each other's rulers squished short or see each other's clocks running slowly, for example. But they will all agree that it takes light the same number of clock ticks to traverse the same number of ruler marks.

jgill

From Einstein's Autobiographical Notes, a thought experiment he had at age 16:

"...a paradox upon which I had already hit at the age of sixteen: If I pursue a beam of light with the velocity c (velocity of light in a vacuum), I should observe such a beam of light as an electromagnetic field at rest though spatially oscillating. There seems to be no such thing, however, neither on the basis of experience nor according to Maxwell's equations. From the very beginning it appeared to me intuitively clear that, judged from the standpoint of such an observer, everything would have to happen according to the same laws as for an observer who, relative to the earth, was at rest. For how should the first observer know or be able to determine, that he is in a state of fast uniform motion? One sees in this paradox the germ of the special relativity theory is already contained."

tim wood

What then of the postulate that the relative velocity of light with respect to an object is "constant"? If I'm travelling in a spaceship with a given velocity, the relative velocity of light with respect to my spaceship will be 300,000 km/h. If I were then to alter my velocity, doesn't the velocity of light have to change accordingly so as to ensure that the relative velocity stays at a constant 300,000 km/h?

What gives? — TheMadFool

There are lots of Youtube videos, not to speak of shelves of books, that can set you straight. And, the speed of light is not just a postulate.

↪Gnomon

No, no, no, no. No!

noAxioms

The great Albert Einstein postulated that the velocity of light is constant at approximately 300,000 km/h. This one postulate and maybe a few more is the allegedly the foundation of his theory of relativity, a theory that has withstood many attempts at disproof. So far so good. — TheMadFool

It's 300,000 km/sec. It's a speed, not a velocity.
The postulate of SR is that that speed will be measured regardless the reference frame used. It doesn't actually posit that the speed actually IS frame invariant, just that it will be measured that way.

Consider 2 cars, A and B, moving on the same practically straight freeway.

1. Situation 1: A is moving at 20 km/h north and B is moving 60 km/h north. The relative velocity of B with respect to A is 60 - 20 = 40 km/h.

Per Einstein, no. Close, but not exactly 40. For instance, scale up the speed to say 0.2c and 0.6c, and the relative velocity of B with respect to A becomes 4/9 c, not 0.4c.

What then of the postulate that the relative velocity of light with respect to an object is "constant"? If I'm travelling in a spaceship with a given velocity, the relative velocity of light with respect to my spaceship will be 300,000 km/h. If I were then to alter my velocity, doesn't the velocity of light have to change accordingly so as to ensure that the relative velocity stays at a constant 300,000 km/h?

Unintuitive, but no. Light speed (not velocity) remains at c relative to anything. This works out if you use the velocity addition formula instead of straight addition like you're doing all through the OP.

Metaphysician Undercover

And, the speed of light is not just a postulate. — tim wood

That the speed of light is the same, relative to any object, is an Einsteinian postulate. If you read his book "Relativity The Special And The General Theory", you'll see that he says we can "stipulate" this, to allow the motion of light to be brought into relativity theory.

tim wood

↪Metaphysician Undercover

Sweet Jesus, MU! No!

From our friend the internet:
"In 1728, English physicist James Bradley based his calculations on the change in the apparent position of the stars due Earth's travels around the sun. He put the speed of light at 185,000 miles per second (301,000 km/s), accurate to within about 1 percent.

And:
"Today, special relativity is proven to be the most accurate model of motion at any speed when gravitational effects are negligible. Even so, the Newtonian model is still valid as a simple and accurate approximation at low velocities (relative to the speed of light), for example, the everyday motions on Earth.

Relativity both general and special are among the most tested and most accurate accounts of anything in science. That's not stipulation, postulate, or opinion; it's a plain fact.

Antediluvian science, you should know, is not quaint; it has no charms. And when offered as current, is a damnable lie, and there are too many of those in the world at the moment. There's no excuse for your ignorance on this - or for such an ignorant comment.

tim wood

Light speed (not velocity) remains at c relative to anything. — noAxioms

Small point. C varies in different media, as through water, and so forth. And, fun fact, when it is slowed through water, then phenomena like Cerenkov radiation actually propagates faster than the light. In a vacuum, though, C is just C. Youtube for lots of videos on these topics.

Metaphysician Undercover

↪tim wood

That's irrelevant, we're talking about whether Einstein did or did not postulate that the speed of light is constant regardless of the relative speed of the object. The answer is yes he did.

There's no excuse for your ignorance on this - or for such an ignorant comment. — tim wood

You're a strange animal too.

tim wood

↪Metaphysician Undercover

Then perhaps you should have written, "

That the speed of light is the same, relative to any object, was an Einsteinian postulate. — Metaphysician Undercover

Verbs matter. Einstein may well have been first, and he may well have stipulated - that's a matter of history - but that's not how it is now.

Metaphysician Undercover

↪tim wood

It's a postulate of Einstein's special theory of relativity, and that's a fact.

You're being ridiculous to argue otherwise.

Metaphysician Undercover

↪tim wood

Regardless of the evidence which supports the postulate, it's still a postulate.

tim wood

↪Metaphysician Undercover

Read your sentence again! "That the speed of light is the same is...." And you might give the OP a closer read too.

Metaphysician Undercover

↪tim wood

Have you got a point?

tim wood

↪Metaphysician Undercover

Not beyond that which was made.

Metaphysician Undercover

↪tim wood

Making a fool of yourself?

tim wood

↪Metaphysician Undercover

I'll let the reader judge.

Metaphysician Undercover

↪tim wood

I am the reader, judgement made.

TheMadFool

It's 300,000 km/sec. It's a speed, not a velocity.
The postulate of SR is that that speed will be measured regardless the reference frame used. It doesn't actually posit that the speed actually IS frame invariant, just that it will be measured that way. — noAxioms

Ok but once you have a frame of reference it becomes relative velocity right? I mean the speed has to be relative to something.

Per Einstein, no. Close, but not exactly 40. For instance, scale up the speed to say 0.2c and 0.6c, and the relative velocity of B with respect to A becomes 4/9 c, not 0.4c. — noAxioms

Thanks but if we apply the relative velocity formula to the situation im which an object A is travelling at a nonrelativistic velocity of a, the equation that gives the relative velocity of light with respect to object A solves to: c = (c - a)/(1 - a/c) = approximately c = c - a where c is the velocity of light. c = c - a is a contradiction!

Pfhorrest

Small point. C varies in different media, as through water, and so forth. And, fun fact, when it is slowed through water, then phenomena like Cerenkov radiation actually propagates faster than the light. In a vacuum, though, C is just C. Youtube for lots of videos on these topics. — tim wood

Isn't it more accurate to say that light travels at less than c through various media, not that c itself becomes less in those media? c is always the speed of light in a vacuum, but light not in a vacuum can travel slower than that.

Also, I don't think it's correct to say that Cerenkov radiation itself propagates faster than light. Rather, Cerenkov radiation is the result of something moving through a medium faster than light moves through that medium. The radiation itself, being light, moves at the speed of light in that medium.

Pfhorrest

Ok but once you have a frame of reference it becomes relative velocity right? I mean the speed has to be relative to something. — TheMadFool

(The post you're replying to was making a point to differentiate velocity from speed. They're not synonyms. But I'm replying to the unrelated point you're making in response).

All velocity is relative velocity, and all speed is relative speed, but the upshot of relativity is that light has the same speed relative to anything. This is because the speed of light is a consequence of the behavior of electromagnetic fields, and the laws governing those don't change just because you're moving relative to something else.

The only way to make sense of that is to suppose that observers moving relative to each other will observe the same pairs of events (points in spacetime) to be separated by different amounts of space and time, so that light can travel at the same speed from one event to the other relative to each observer, even though each observer is moving differently.

As it turns out, they do. For example, clocks in satellites (which are moving very fast, in order to stay in orbit) run at different rates than clocks on the ground, and we have to take account of that to do things like GPS tracking, which depend on timing signals from satellites.

c = (c - a)/(1 - a/c) = approximately c = c - a where c is the velocity of light. c = c - a is a contradiction! — TheMadFool

Not when a = 0, and 'approximately c' = c - a precisely when a = 'approximately 0', i.e. nonrelativistic speeds. (All nonrelativistic speeds are 'approximately 0' on the scale of relativistic speeds).

TheMadFool

light has the same speed relative to anything. — Pfhorrest

That is relative velocity

Not when a = 0, and 'approximately c' = c - a precisely when a = 'approximately 0', i.e. nonrelativistic speeds. (All nonrelativistic speeds are 'approximately 0' on the scale of relativistic speeds). — Pfhorrest

That's when the object's at relative rest. No problem with that.

SophistiCat

↪TheMadFool

What you call "relative velocity" does not apply in Special Relativity. You need to understand how velocity addition works in Minkowski spacetime. These are the very basics of the theory, and until you understand them you cannot talk about any "paradoxes." Don't be lazy, do your homework instead of expecting people to spoon-feed this to you.

Light velocity paradox

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