Equivalence between a Black Hole and travelling at the speed of light

Pierre007080

Hi JesseM. Thanks for your reply. I think that I am following now. There are two questions that I would like to ask:
• The beam travelling horisontally across the room bends down from the gravity … if it was travelling vertically upwards (directly away from the centre of the large mass) would the wavelength be shortened compared to if the room was further away form the mass? In fact, if we were at (or near) the event horison would the wavelength not be almost infinitely shortened? The observer in the room would not realise it because his ruler would also be shortened? (This is what confused me into thinking that the situation was equivalent to someone travelling at speed trying to measure his shortened wavelength in the direction of travel with his shortened ruler)
• The mass on the trampoline analogy. The implication as I understand it is that a rolling ball would go down the gradient along a line that depended how it approached the depression and at what speed. We are used to seeing geographical maps that show isobars (pressure or height etc). These do not primarily show the path water etc would flow but join points of equal potential. If the trampoline analogy was viewed as layers of iso-potential (gravity or density???) in 3D would the picture not be one of concentric iso-potential spheres around the massive object?
Kind regards.
Hi there Guys. I have quoted my two questions that I asked to return to. Maybe my first does refer to gravitational redshift, but surely the shortened wavelength due to gravity(???this was my question) would rather be a blueshift???

I read the comments about the trampoline analogy and just read about how it depicts time and GR ... sorry guys, I must be blinder than I thought. I need more guidance than that please.

Dale

Mentor
Maybe my first does refer to gravitational redshift, but surely the shortened wavelength due to gravity(???this was my question) would rather be a blueshift???
Red or blue depends on if the light is going up or down. If the transmitter is lower than the receiver then there is a redshift. If the transmitter is higher than the receiver then there is a blueshift.

Pierre007080

I think I understand that, but I thought that the redshift was due to the time dilation ... what I am trying to get at is that wavelength is SHORTENED due to gravity. I understood that the redshift was made up of a SHORTENED wavelength, but because time dilation escalates more quickly than the rod (or in this case wave) shortening as we get nearer to the mass, the overall effect would be one of redshift???

A.T.

I read the comments about the trampoline analogy and just read about how it depicts time and GR ... sorry guys, I must be blinder than I thought. I need more guidance than that please.
The point is, that the trampoline analogy doesn't depicts how gravity works in GR. Follow the links in this post for better analogies:

Pierre007080

I agree with some of the guys that the trampoline analogy says very little except to show that space can warp. It gives no three dimensional depiction and certainly no time reference.

Pierre007080

DaleSpam and JesseM it seems as though you have abandoned me?? There seems to be consensus that gravitational redshift would be caused by time dilation, but the question remains: is the wavelength shortened by gravity if the wave is leaving a massive object along ta radial?

JesseM

DaleSpam and JesseM it seems as though you have abandoned me?? There seems to be consensus that gravitational redshift would be caused by time dilation, but the question remains: is the wavelength shortened by gravity if the wave is leaving a massive object along ta radial?
No, "gravitational redshift" deals precisely with the issue of light emitted from a point closer to the source of gravity to a point farther from the source, and it says that the wavelength is lengthened, not shortened.

Pierre007080

Red or blue depends on if the light is going up or down. If the transmitter is lower than the receiver then there is a redshift. If the transmitter is higher than the receiver then there is a blueshift.
This comment of yours has been worrying me. If redshift is caused by time dilation, then the direction should surely not matter?

JesseM

This comment of yours has been worrying me. If redshift is caused by time dilation, then the direction should surely not matter?
Gravitational time dilation in GR isn't normally symmetrical the way velocity-based time dilation in SR is...the lower clock will see the higher clock running faster than his own, while the higher clock will see the lower clock running slower than his own, and if they both use Schwarzschild coordinates they'll both agree the lower clock goes through fewer ticks than the higher one in any given interval of coordinate time.

Dale

Mentor
DaleSpam and JesseM it seems as though you have abandoned me?? There seems to be consensus that gravitational redshift would be caused by time dilation, but the question remains: is the wavelength shortened by gravity if the wave is leaving a massive object along ta radial?
If the wave is leaving a massive object then it is going up to a higher gravitational potential. This means that it is losing energy. Therefore the frequency becomes lower (redshift). Because the frequency is lower and c is constant the wavelength must be longer than when it was emitted.

Pierre007080

Gravitational time dilation in GR isn't normally symmetrical the way velocity-based time dilation in SR is...the lower clock will see the higher clock running faster than his own, while the higher clock will see the lower clock running slower than his own, and if they both use Schwarzschild coordinates they'll both agree the lower clock goes through fewer ticks than the higher one in any given interval of coordinate time.
Thanks JesseM. I need to read up about Schwarzchild coordinates and digest your answer. Where can I read more on GR time dilation not being symmetrical like velocity based time dilation?

Pierre007080 If the wave is leaving a massive object then it is going up to a higher gravitational potential. This means that it is losing energy. Therefore the frequency becomes lower (redshift). Because the frequency is lower and c is constant the wavelength must be longer than when it was emitted.
Thanks DaleSpam. This may be basic for you, but this has really helped me. Is it also true that the wavelength from some atomic oscillation would be shorter if the mass from which it is being emitted is larger.

Pierre007080

Thanks JesseM. I need to read up about Schwarzchild coordinates and digest your answer. Where can I read more on GR time dilation not being symmetrical like velocity based time dilation?
Okay JesseM, youv'e scared me again. There is so much mathematics and terms like pseudo-Riemannian stuff that there is no way that I can see the light about why there is not symmetry in GR time dilation. Surely the radius from the centre of the mass is the main criterion as to the extent of GR time dilation and rod shortening? Spherical symmetry also sound sensible ... the concept of nested spheres satisfying Einsteins field equations sounds vaguely sensible, but I'm sure a more simplistic explanation is possible for us normal people????? Perhaps the SR analogy of time dilation and rod shortening IS appropriate as an APPROXIMATION of the GR effects near of massive objects???????

Pierre007080 If the wave is leaving a massive object then it is going up to a higher gravitational potential. This means that it is losing energy. Therefore the frequency becomes lower (redshift). Because the frequency is lower and c is constant the wavelength must be longer than when it was emitted.
If I understand this correctly a continuously emitting EM waveset would exhibit a short wavelength near the mass and an increasingly longer wavelength further away? This would surely be spherically valid at a set radius?

Dale

Mentor
Is it also true that the wavelength from some atomic oscillation would be shorter if the mass from which it is being emitted is larger.
Are you thinking of something like a spring-mass system at an atomic level, or are you thinking more about something like the hyperfine transition that defines an atomic clock.

If I understand this correctly a continuously emitting EM waveset would exhibit a short wavelength near the mass and an increasingly longer wavelength further away?
Yes.

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Pierre007080

Are you thinking of something like a spring-mass system at an atomic level, or are you thinking more about something like the hyperfine transition that defines an atomic clock.

DaleSpam, you are going where I fear to tread. I was trying to find a way to ask what would happen if the mass increased and the emission was from the same source as it would have been when the mass were smaller. Perhaps black body radiation from two massive bodies that have co-incidently reached the same temperature???

Dale

Mentor
Blackbody radiation is a function of temperature only. It does not depend on the mass of the object nor on the mass of its constituents.

If you are trying to ask whether or not gravitational time dilation could be interpreted as increased mass, then I think the answer is "not in general". In other words, there may be some specific cases where you could (e.g. mass/spring system) but many cases where you could not (e.g. pendulum or blackbody).

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Austin0

Blackbody radiation is a function of temperature only. It does not depend on the mass of the object nor on the mass of its constituents. If you are trying to ask whether or not gravitational time dilation could be interpreted as increased mass, then I think the answer is "not in general". In other words, there may be some specific cases where you could (e.g. mass/spring system) but many cases where you could not (e.g. pendulum or blackbody).
Would it or not be dependant on the gravitational altitude of its location?

Dale

Mentor
Would it or not be dependant on the gravitational altitude of its location?
Yes. Or rather, the spectrum received would depend on the temperature of the blackbody and the gravitational time dilation between the blackbody and the receiver. The time dilation then is dependant on the difference in "gravitational altitude".

Austin0

Yes. Or rather, the spectrum received would depend on the temperature of the blackbody and the gravitational time dilation between the blackbody and the receiver. The time dilation then is dependant on the difference in "gravitational altitude".
Thanks

Is there any way to measure electron resonance frequencies other than by the frequency of light they can absorb??

Pierre007080

Blackbody radiation is a function of temperature only. It does not depend on the mass of the object nor on the mass of its constituents.

I think that I put my question poorly. The fact that I referred to blackbody at the same temp was to get the same emission frequency from two massive objects of differing masses. The question is this: If we were to measure the wavelength of the emitted ray at the same distance from the centre of the two bodies, would the wavelength of the radiation from the more massive body be shorter?

Pierre007080

Gravitational time dilation in GR isn't normally symmetrical the way velocity-based time dilation in SR is...the lower clock will see the higher clock running faster than his own, while the higher clock will see the lower clock running slower than his own, and if they both use Schwarzschild coordinates they'll both agree the lower clock goes through fewer ticks than the higher one in any given interval of coordinate time.
I think I understand. Symmetry is being used in a way that I'm unsure of. Do you mean that in SR the sum of velocities is different of that of GR. In other words the time dilation and rod shortening in GR are the same for any observer whereas those of SR are relative to the observer's motion?

Dale

Mentor
If we were to measure the wavelength of the emitted ray at the same distance from the centre of the two bodies, would the wavelength of the radiation from the more massive body be shorter?
No, the wavelength from the more massive body would be longer. I refer you back to post 35.

If the wave is leaving a massive object then it is going up to a higher gravitational potential. This means that it is losing energy. Therefore the frequency becomes lower (redshift). Because the frequency is lower and c is constant the wavelength must be longer than when it was emitted.
For the more massive body the change in gravitational potential is greater so the redshift is greater so the frequency is lower so the wavelength is longer.

Pierre007080

No, the wavelength from the more massive body would be longer. I refer you back to post 35.

For the more massive body the change in gravitational potential is greater so the redshift is greater so the frequency is lower so the wavelength is longer.
This seems like a contradiction to me. Please bear with my persistence as this is important to my understanding of GR. May I restate the question in the following way: If we were on two massive bodies of exactly the same size (radius) but different masses and we're standing on the surface. Would the black body radiation emitted radially (away from the centre of the mass) from two similar items be emitted at the same wavelength and frequency?

Dale

Mentor
If we were on two massive bodies of exactly the same size (radius) but different masses and we're standing on the surface. Would the black body radiation emitted radially (away from the centre of the mass) from two similar items be emitted at the same wavelength and frequency?
This is going in circles. Why don't you try to answer this question (frequency of emitted radiation) with what I have already provided (see post 42). Then try to answer the question about what would the frequency of the received radiation be (see post 35) with the hopefully obvious stipulation that the receiver will be above the blackbody surface.

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