Understanding the Doppler Effect in Space-time Curvature

[ATdisplays]

I have a question that has been bugging me for a while. You see, I have a predisposition of trying to visualize everything that I learn. I have no problem visualizing space-time, black-holes distorting space-time, the universe expanding, etc..., but when it comes to the Doppler Effect I want to double check what I think I'm mentally seeing is what actually happens in reality.

For example, imagine you have a police car sounding off it's siren and speeding at 100/mph towards and you're walking on the side of the road. As that police car is getting closer and closer the pitch of the sirens will sound like its going higher in pitch. But when the police car passes you the pitch will drop all of a sudden. Basically the sound waves in front of the police car are compressed and the sound waves behind it are less compressed. Same thing with a boat creating waves in water.

So in the air, the Doppler Effect was due to compression along the direction of motion and decompression behind it. Long story short, when dealing with light is the Doppler Effect due to compression of space-time in front of the accelerating object and decompression of space-time behind it or what?

Like Einstein pointed out, an object accelerating through space-time will gain mass and time for that object will slow down. I just want to know what's happening to the space-time around that object that is accelerating. Hope the question makes sense

 

[pervect]

I don't think of either case as involving compression. If the police car was a big, flat, box, yes, it would create a big pressure wave in front of it. But if it was sleek and streamlined, it would pass through the air without creating much of a pressure wave. However, in either case, you'd still have the doppler effect, so the pressure wave seems like an irrelevant side-effect to me.

 

[ATdisplays]

I kinda got a clue of what you're talking about, but I don't completely understand it just yet. Coming back to Doppler Effect and sound, if that police car was moving at 100/hr then the speed of sound from the sirens would not be 868/mph (speed of sound 768/mph + speed of the police car 100/mph) when it's coming towards you or 668/mph when it's going away from you. In either scenario the speed of sound stays the same at 768/mph, but the pitch of the sirens changes relative to where you're hearing the sound from the car. This will happen regardless of the shape or size of the object (imagine the sound of a bullet ricochet ). Those sound waves coming from the sirens are caused by alternating waves of compression and rarefaction (or drop in air pressure). This little old video from 1933 explains that perfectly around 1:30mins into it

So as an object is moving in space, is it slightly compressing or altering the space-time in front and behind it? Because if nothing is happening to the space-time around that object then the light coming out of it should be unchanged to any observer regardless of the object's direction of motion. But for you to see a red-shift/blue-shift from that object, something has to be happening to the immediate space-time around that object for those changes to occur. Not trying to be stubborn, but I want to get my thoughts in order/clarified

 

[Mentz114]

So as an object is moving in space, is it slightly compressing or altering the space-time in front and behind it?

No. Space-time is not a physical medium. Also only relative velocity can be defined, there is no absolute velocity defined wrt spacetime. If the emitter is is moving relative to the receiver, there is a doppler effect. But another observer, moving differently relative to the emitter sees a different Doppler effect. The light is unchanged, the frequency shift depends only on relative velocity.

 

[pervect]

Sound travels through a physical medium. So it means something to compress a physical medium, you can test it with a pressure meter. And because it's a medium, sound travels through it and has a definite speed relative to the medium.

Space isn't generally regarded as a physical medium nowadays. You can't really tell if it's 'compressed' or not compressed by experiment. At least not from what I've seen.

It won't necessarily hurt anything if you think of , Lorentz contraction, for instance, as being compressed space. (Unless I"m misunderstanding what you mean, which is possible, it's a little vague).

But it's not generally the way that most people think of space nowadays - as far as I can tell, at least, I haven't tried to take a poll or anything.

For the most part, it's regarded as not being real, because you can't objectively measure it's compression, there isn't any such thing as a "space-compression" meter.

I think Bell was a proponent of thinking of atoms as compressing when in motion, so you aren't the only one with this approach.

So, from my point of view, "space compression" is mostly philosophical baggate that doesn't really matter one way or the other to anything one can actually measure. If it helps you to understand things, it might not do any harm, but it might also get in the way someday, having to metaphorically "lug it along".

 

[chogg]

Space isn't generally regarded as a physical medium nowadays. You can't really tell if it's 'compressed' or not compressed by experiment. At least not from what I've seen.

Ah, but what about General Relativity? Couldn't we understand variations in the metric as a compression (or expansion) of spacetime?

LIGO is an example of an experiment whose purpose is to detect compressions in spacetime (gravitational waves), if my understanding is correct.

 

[bcrowell]

Ah, but what about General Relativity? Couldn't we understand variations in the metric as a compression (or expansion) of spacetime?

LIGO is an example of an experiment whose purpose is to detect compressions in spacetime (gravitational waves), if my understanding is correct.

The OP was trying to analyze electromagnetic waves, not gravitational waves. (Even in the case of gravitational waves, there is no such thing as a compression of space. Gravitational waves are transverse, not longitudinal. If you try to write down a metric representing a longitudinal gravitational wave, you get something that is just flat spacetime that has been described in funny coordinates.)

 

[ATdisplays]

Thanks for that observation chogg because I completely forgot about LIGO. Then my question would be if space-time is not a physical medium then why would they try to detect the gravitational waves in space-time?

From understanding of LIGO if I remember it right, they setup a laser interference pattern from an X direction and a Y direction ( I think kinda like the Michelson-Morley experiment) and if there is an incoming gravitational wave then it should contract space/space-time in one direction more than the other causing a shift in the interference pattern.

For the gravitational waves to propagate through space and be detected by LIGO, they would need some kind of a medium to propagate in, right? You wouldn't expect sound waves to propagate in a vacuum since you need air/liquid for those waves to propagate in them. If the assumption is that space-time is not a physical medium then why waste time/money/resources on an experiment that depends on their to be a vacuum?

 

[ghwellsjr]

Why do you think gravity would be any different than light, in terms of its propagation requiring a medium? The issue is whether the influence of an accelerating mass is propagated at infinite speed, aka action-at-a-distance as Newton proposed, or at some finite speed such as c, just as light waves are created by accelerated charges.

 

[bcrowell]

Thanks for that observation chogg because I completely forgot about LIGO. Then my question would be if space-time is not a physical medium then why would they try to detect the gravitational waves in space-time?

From understanding of LIGO if I remember it right, they setup a laser interference pattern from an X direction and a Y direction ( I think kinda like the Michelson-Morley experiment) and if there is an incoming gravitational wave then it should contract space/space-time in one direction more than the other causing a shift in the interference pattern.

For the gravitational waves to propagate through space and be detected by LIGO, they would need some kind of a medium to propagate in, right? You wouldn't expect sound waves to propagate in a vacuum since you need air/liquid for those waves to propagate in them. If the assumption is that space-time is not a physical medium then why waste time/money/resources on an experiment that depends on their to be a vacuum?

In fact the main purpose of LIGO is not to verify that gravitational waves exist, because we already know that based on empirical data: http://en.wikipedia.org/wiki/PSR_B1913+16 The main purpose of LIGO is to try to do astronomy using gravitational waves. In any case, as ghwellsjr has pointed out, waves don't have to have a medium, so the existence of gravitational and electromagnetic waves has nothing to do with the (vaguely defined) idea that space is a "physical medium." If that doesn't satisfy you and you want to continue this thread, please give us an operational definition of what you mean by "physical" and "medium."

 

[GrayGhost]

Couldn't we understand variations in the metric as a compression (or expansion) of spacetime?

Sure. But just like Maxwell and Einstein, no one has the proof of what the medium is. Best not to mention it in your theory if you cannot define its nature. Fields may well be variations and configurations of the medium within the medium (ie energy forms), and nothing more. We cannot see the medium, except for the variations and configurations within it. Here's the problem though ... physics is definable via said variations/configurations without any description of the underlying medium whatever (at least so far). IOWs, fields alone get the job done. So physics works whether the fields exist unto themselves, versus existing as aspects of an underlying medium. So by Occam's razor, we ignore any such medium's existence until there's a good reason to assume otherwise. IMO though, it is more reasonable to assume a medium exists, than does not. There is no harm in assuming a medium exists, so long as its nature upholds physics. It would surely not ba of classical fluid nature, this much is certain. And, said medium would possesses no absolute reference for motion, as relativity shows. There are surely reasons to assume a medium exists, however I suppose they do not carry enough weight (to date) for the scientific community at large.

GrayGhost

 

[pervect]

Thanks for that observation chogg because I completely forgot about LIGO. Then my question would be if space-time is not a physical medium then why would they try to detect the gravitational waves in space-time?

From understanding of LIGO if I remember it right, they setup a laser interference pattern from an X direction and a Y direction ( I think kinda like the Michelson-Morley experiment) and if there is an incoming gravitational wave then it should contract space/space-time in one direction more than the other causing a shift in the interference pattern.

For the gravitational waves to propagate through space and be detected by LIGO, they would need some kind of a medium to propagate in, right? You wouldn't expect sound waves to propagate in a vacuum since you need air/liquid for those waves to propagate in them. If the assumption is that space-time is not a physical medium then why waste time/money/resources on an experiment that depends on their to be a vacuum?

There isn't any way that I'm aware of to measure the compression of space, which was the original topic. However it *is* possible for space to curve (and space-time as well), and this CAN be measured.

The usual way of measuring such curvature detects tidal forces. This sort of measurement is done routinely, for instance in oil exploration, with "full-tensor gravimeters".

As has been mentioned, the gravity waves are not compression waves. You can think of them as "ripples in space-time" if you use the ever-popular and sometime misleading picture of envisioning space-time as a 2 dimensional sheet.

You don't really need any sort of "physical medium" to propagate gravitational waves - you do need, however, the fact that space-time has curvature.

 

[chogg]

I don't think of spacetime as a physical medium -- i.e. as "stuff". It's where the "stuff" lives, the backdrop to all the action. Yet spacetime clearly has nontrivial properties. We can interact with it, bend it. It even (theoretically) admits topologically interesting configurations, such as wormholes.

A gravitational wave passing through Earth, with nonzero components along a LIGO arm, will change the distance between the ends of that arm. Nothing has moved within spacetime as a result of that wave; rather, the spacetime distance itself -- the metric -- has changed. I don't see why we can't think of that as a compression of spacetime.

I know it's nothing to do with the OP, but I wasn't actually responding to the OP. I was more interested in whether GR let's us view spacetime as a medium of some kind. Although rereading the post I responded to, I think it was a mistake to respond the way I did. It makes it sound like I think spacetime is a physical medium -- some kind of "stuff", like maybe there are "spacetime particles" there to propagate the waves. No: I'm perfectly comfortable with medium-less propagation of waves. But if spacetime carries a metric which varies from point to point, I don't see the harm in thinking of it as "something like" a medium (as long as we are careful to emphasize the differences with every other medium we have encountered).

 

[bcrowell]

A gravitational wave passing through Earth, with nonzero components along a LIGO arm, will change the distance between the ends of that arm. Nothing has moved within spacetime as a result of that wave; rather, the spacetime distance itself -- the metric -- has changed. I don't see why we can't think of that as a compression of spacetime.

It's a transverse wave. If the wave is propagating along the x axis, and the arm along the y-axis shrinks, then a similar arm along the z axis simultaneously expands by the same ratio. The volume stays the same. (That kind of volume conservation is essentially what distinguishes the part of the curvature measured by the Ricci tensor from the rest of it.) That's why I wouldn't call it a compression. A sound wave, which is longitudinal, is a compression wave.

And to described in more detail the other point in #7, say you write down a metric like ds²=dt²-(1+Asin kx)dx²-dy²-dz². This metric looks like one describing a spacetime in which the x-axis is getting alternately compressed and expanded. But in fact if you compute the curvature of this spacetime, it's zero. You can change it to Minkowski space with a change of coordinates.

As another example, take the metric ds²=dt²-4dx²-dy²-dz². This does not represent a spacetime in which the x-axis is somehow physically compressed or expanded. This is just Minkowski space described in funny coordinates. The type of compression or expansion measured by one of the arms of LIGO is not detectable by itself, even in principle. It's only detectable through its relation to what's going on along other axes of space and/or time.

This is why nobody talks about "spacetime compression," only spacetime curvature.

 

[chogg]

Ah, now I see. When I say "compression", you think "longitudinal". I was visualizing a transverse wave the whole time, but I don't think I ever made that explicit. (Gravitational waves were my oral qualifier topic, though obscured now by several years' worth of rust.)

Your subsequent examples were helpful in explaining why curvature is a more appropriate concept than compression in the case of spacetime. Thanks!