# Length contraction, hubble constant, and C

• brainstorm
In summary, the speed of light is invariant in any frame, but objects approaching the speed of light experience length contraction and time dilation, allowing them to travel at the same ratio to the speed of light. This means that in an accelerated frame, the scale of the universe would shrink, allowing an object like the Hubble telescope to see more distant galaxies than from its Earth orbit. The concept of "dilation" refers to this effect, where scale and time relative to light-distance decrease with object-velocity increase. The speed of light must be measured locally, even in a gravitational field, as the time dilation affects the measurement of time and light.
brainstorm
Question: As an object approaches C and its length contracts, does space-time contract also, causing the a larger range of the universe to become visible? I.e. if the Hubble space telescope was traveling at high velocity, would it gain access to light from more distant galaxies than it has from its Earth orbit?

2) If length contracts with velocity, does the m/s of the speed of light apply in contracted meters and seconds? If so, it would seem that objects could never exceed C in their own frame, but that the object could exceed C from the perspective of slower moving frames.

An object accelerating at a constant rate, for example, could experience time dilation and length contraction in such a way that the universe would change scale for it. At the same time, the object may enter into a context with other objects moving at comparable speed and dilation.

This sounds like sci-fi or crackpottery to me, but I don't see why the speed of light wouldn't reset to the length contraction and dilation levels of an accelerated frame. How could light travel any slower relative to one frame than another?

brainstorm said:
Question: As an object approaches C and its length contracts, does space-time contract also, causing the a larger range of the universe to become visible? I.e. if the Hubble space telescope was traveling at high velocity, would it gain access to light from more distant galaxies than it has from its Earth orbit?
No - take the object to be a photon.It hardly affects space-time.
If a massive body is traveling at a speed close to c , its energy would be high enough to bend the light of its surroundings inward ( as in a black hole) ; let alone the light from a long distance.

brainstorm said:
2) If length contracts with velocity, does the m/s of the speed of light apply in contracted meters and seconds? If so, it would seem that objects could never exceed C in their own frame, but that the object could exceed C from the perspective of slower moving frames.
Yes , c is invariant. However, the formula for the addition of relativistic velocities shows that the relative speed never exceeds c in any frame.

Eynstone said:
No - take the object to be a photon.It hardly affects space-time.
If a massive body is traveling at a speed close to c , its energy would be high enough to bend the light of its surroundings inward ( as in a black hole) ; let alone the light from a long distance.
Nevermind photons. I think their size remains the same relative to whatever frame they're in. As for matter approaching C, how would it curve spacetime?

Yes , c is invariant. However, the formula for the addition of relativistic velocities shows that the relative speed never exceeds c in any frame.

Right, but what does that mean exactly? Does it mean that C is an absolute velocity measured from a certain gravitational context, e.g. Earth's at sea-level? Or does it mean that in any context of gravity and/or velocity, C is measured relative to length and time in that context?

I believe the answer is the latter, since it doesn't make sense for light to be traveling slower or faster within a frame based on the frames gravitational or velocity relationship with another frame.

What happens, imo, is that as something approaches C its length contracts relative to its surroundings and spacetime dilates relative to it. That way it continues to travel at the same ratio to C, only C now refers to an extended field. Thus, for example, if the Hubble telescope was approaching C, it would see more distant galaxies than it does in Earth orbit because the scale of the universe would shrink relative to its accelerated speed.

I believe that "dilation" refers to this effect, which correlates with length-contraction since scale and time relative to light-distance decrease with object-velocity increase. Put it this way: frame speed increases, which increases light-range per unit-time, but size of objects decrease because they are moving faster relative to each other, which means they have to gain gravitational distance to each other even while their light-distance is remaining constant or decreasing.

brainstorm said:
Nevermind photons. I think their size remains the same relative to whatever frame they're in. As for matter approaching C, how would it curve spacetime?

If the size of a photon is measured by wavelength, doesn't the size of a photon change exactly as predicted by the length contraction of relativity?

brainstorm said:
Right, but what does that mean exactly? Does it mean that C is an absolute velocity measured from a certain gravitational context, e.g. Earth's at sea-level? Or does it mean that in any context of gravity and/or velocity, C is measured relative to length and time in that context?

I believe the answer is the latter, since it doesn't make sense for light to be traveling slower or faster within a frame based on the frames gravitational or velocity relationship with another frame.

Doesn't the speed of light need to be measured locally? Even in a gravity well the low intensity of Earth the changes in the speed of light due to vertical separation are (with great care) measurable.

Since time is dilated in a gravitational field, the time a light pulse would reflect between two mirrors a fixed distance apart would increase the further into a well an outside observer looks. This would be countered exactly by the time dilation of a local observer, but all observers would observe that clocks further out of a well run faster than those in the well.

brainstorm said:
Question: As an object approaches C and its length contracts, does space-time contract also, causing the a larger range of the universe to become visible? I.e. if the Hubble space telescope was traveling at high velocity, would it gain access to light from more distant galaxies than it has from its Earth orbit?

Oddly enough, if the telescope is moving at relativistic velocities towards a distant galaxy, the galaxy would appear smaller (and further away) due to abberation effects. On the other hand, the photons arriving at the film or ccd backplate of the telescope would appear to be arriving at a higher rate per second, so the the galaxy would appear to be brighter and smaller at the same time. There would also be a Doppler effect that makes the photons seem more energetic or shifted towards the blue end of the spectrum. (i.e. the wavelength of the photons appears shorter.) The light that the telescope "has access to" remains the same, whatever the relative velocity of the telescope is to the source. It just sees the light in a different way.

kev said:
Oddly enough, if the telescope is moving at relativistic velocities towards a distant galaxy, the galaxy would appear smaller (and further away) due to abberation effects. On the other hand, the photons arriving at the film or ccd backplate of the telescope would appear to be arriving at a higher rate per second, so the the galaxy would appear to be brighter and smaller at the same time. There would also be a Doppler effect that makes the photons seem more energetic or shifted towards the blue end of the spectrum. (i.e. the wavelength of the photons appears shorter.) The light that the telescope "has access to" remains the same, whatever the relative velocity of the telescope is to the source. It just sees the light in a different way.

I guess the more distant galaxies would become visible due to blue-shift counteracting the red-shift caused by universal expansion.

It also seems that the speed of universal expansion can never exceed the speed of light in the frame of two galaxies moving in relation to each other. That lends more support to my belief that dilation is compensation for the relative limit of C, in that the two galaxies expanding away from each other would have to be approaching C and, in addition to red-shifting, the speed of light between those two galaxies would have to be faster than between two galaxies expanding apart at slower relative speed.

Another way to put it would be to say that more distant galaxies become visible at a higher wavelength as velocity increases and/or gravity decreases. This seems to be the same thing as saying that spacetime is dilating to include more contents.

Now consider the same logic from the perspective of an object in a black hole. As the object enters the black hole, spacetime contracts rendering the inside of the black hole as vast as the Hubble constant. Light cannot escape because its speed/momentum is fixed relative to the gravity-dilation levels and velocities of objects within the BH. However, an object able to accelerate to increasingly accelerated frames would see spacetime expand to the point that objects outside the black hole would become more accessible.

I can't decide whether these objects then become accessible from the black hole, but if they do it might just be because these objects are already headed for the event horizon and their time relative to that inside the BH is vastly accelerated. So objects outside the BH might be accessible to those inside the BH only because they are themselves entering it at some future moment.

Do you see why I equate the behavior of spacetime inside the Hubble constant as how it would be experienced from inside a BH, considering the relative contraction of space and slowing of time relative to contracted space? In other words, I suspect matter-energy relations to appear the same to an observer within the BH as they appear to the same observer outside the BH when she is outside it.

I also tend to then think that the fact of universal expansion gives each point in the universe its own Hubble constant horizon, which from outside that horizon appears to be the horizon of a black hole. I suppose the correlate of this would be that the outskirts of the Hubble constant as viewed from our velocity/gravity context is indistinguishable from if that edge was completely composed of black holes.

In other words, the ratio of gravity/velocity to C for anything depends on its distance from the observer. Likewise, gravity and velocity are essentially the same thing in that velocity high enough to dilate spacetime in one frame is necessarily pivoting relative to some gravitational fulcrum that corresponds to a gravitational field strong enough to include the object approaching C.

This fulcrum would not have to be a single star or even galaxy. It could be a constellation of galaxies. The point is that in the frame that includes the object approaching C and its gravitational fulcrum, the object is approaching the horizon at which light can no longer escape the fulcrum (hubble constant), which would correspond to the Zwarschild radius from the inside of a black hole.

## 1. What is length contraction?

Length contraction is a phenomenon in special relativity where an object's length appears shorter when it is moving at high speeds relative to an observer. This is due to the fact that time and space are relative and can appear differently to different observers.

## 2. How does the Hubble constant relate to the expansion of the universe?

The Hubble constant is a measure of the rate at which the universe is expanding. It is used to determine the age and size of the universe, as well as its future expansion. It is named after Edwin Hubble, who first discovered the relationship between the distance of galaxies and their redshift, which led to the discovery of the expanding universe.

## 3. What is the significance of the speed of light (C) in physics?

The speed of light (C) is a fundamental constant in physics that represents the maximum speed at which all energy, matter, and information can travel in the universe. It plays a crucial role in Einstein's theory of relativity, and is used in many equations to calculate the relationships between time, space, and matter.

## 4. Can length contraction and the Hubble constant be observed in everyday life?

No, these phenomena are only observable at extremely high speeds or on a cosmic scale. For example, length contraction can only be seen in objects moving at a significant fraction of the speed of light, and the effects of the Hubble constant can only be observed in objects very far away, such as galaxies.

## 5. How do length contraction, the Hubble constant, and the speed of light (C) impact our understanding of the universe?

These concepts are all fundamental to our understanding of the universe and how it behaves. Length contraction helps explain the relationship between time and space, the Hubble constant gives us insight into the expansion of the universe, and the speed of light allows us to make calculations and predictions about the behavior of matter and energy. Without these concepts, our understanding of the universe would be incomplete.

• Special and General Relativity
Replies
63
Views
3K
• Special and General Relativity
Replies
14
Views
299
• Special and General Relativity
Replies
10
Views
473
• Special and General Relativity
Replies
38
Views
3K
• Special and General Relativity
Replies
45
Views
2K
• Special and General Relativity
Replies
54
Views
611
• Special and General Relativity
Replies
12
Views
769
• Special and General Relativity
Replies
7
Views
996
• Special and General Relativity
Replies
17
Views
740
• Special and General Relativity
Replies
29
Views
1K