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

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 for your response. I have re-read the previous discussion but the discrepancy seems to be that I am under the impression that time (the tick of the clock) exists with regard to the "gravitational potential". The "tick of the clock" surely has to be slower at the higher "gravitational potential" on the surface of the larger mass? The "dilation" depends upon the movement of the wave to a higher "gravitational potential". The reason I chose the surface of two same size objects as my reference frame was to eliminate the movement (or dilation) aspect and focus on the fact that the larger mass has a HIGHER gravitational potential at it's surface and that the EMISSION frequency and wavelength would differ as observed by a distant observer at right angles to the emission, even though the temperature of the body is the same. Of course both local parties would measure the frequency as that typical of the black body radiation spectrum.

Dale
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the larger mass has a HIGHER gravitational potential at it's surface
No, the larger mass has a lower gravitational potential (more negative) at its surface. This is the case in Newtonian gravity as well as in the Schwarzschild metric in GR.

the EMISSION frequency and wavelength would differ as observed by a distant observer
This is self-contradictory. Only a local observer can measure the emission frequency. (Actually, even a local observer technically still measures a received frequency, but there are no relative Doppler or time dilation effects for a local observer so a local observer always receives the same frequency as emitted.)

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No, the larger mass has a lower gravitational potential (more negative) at its surface. This is the case in Newtonian gravity as well as in the Schwarzschild metric in GR.

My mistake. The gravitational potential is "lower" at the surface of the more massive body. Will a clock not tick slower near the large mass?

This is self-contradictory. Only a local observer can measure the emission frequency. (Actually, even a local observer technically still measures a received frequency, but there are no relative Doppler or time dilation effects for a local observer so a local observer always receives the same frequency as emitted.)
I understand the local observer point of view, but why should there not be a distant observer at a different gravitational potential viewing the wave emission from the side?

Dale
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why should there not be a distant observer at a different gravitational potential viewing the wave emission from the side?
Certainly you can have such an observer. That would not change anything I said above.

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.
From JesseM's explanation I understood that a distant observer would be able to tell that the lower (Lower gravitational potential) observer would have a clock ticking slower?

Dale
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From JesseM's explanation I understood that a distant observer would be able to tell that the lower (Lower gravitational potential) observer would have a clock ticking slower?
Yes.

Yes.
Why then could a third observer at right angles to the waveset not view both the first two observers (at the low and high gravitational potentials) and recognise that they are experiencing different wavelengths of the same waveset?

Dale
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I don't know what you mean by that. What is a waveset? What does it mean to experience a wavelength of a waveset?

Originally Posted by Pierre007080
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.[/QUOTE]

This is self-contradictory. Only a local observer can measure the emission frequency. (Actually, even a local observer technically still measures a received frequency, but there are no relative Doppler or time dilation effects for a local observer so a local observer always receives the same frequency as emitted.)[/QUOTE]

Hi DaleSpam, It is this previous quote of yours that I am trying to get my head around by suggesting a third observer. I can't understand how you can state that only a local observer can measure the emmission frequency.

Would a third observer not measure a DIFFERENT emission frequency and spectrum from the same temperature black body on the surface of two bodies of different mass because of the different "gravitational potential".

Dale
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OK, let's simplify things. Instead of talking about measuring an emitted frequency lets only talk about emitting or receiving a frequency. Let's stipulate that you can perfectly determine the emitted frequency (e.g. using an ideal clock and an ideal waveform synthesizer) and that you can perfectly determine the received frequency (e.g. with an ideal noise free detector and an ideal clock).

Can you re-ask your question in those terms.

OK, let's simplify things. Instead of talking about measuring an emitted frequency lets only talk about emitting or receiving a frequency. Let's stipulate that you can perfectly determine the emitted frequency (e.g. using an ideal clock and an ideal waveform synthesizer) and that you can perfectly determine the received frequency (e.g. with an ideal noise free detector and an ideal clock).

Can you re-ask your question in those terms.
Hi DaleSpam. Thanks for your attempts to help me. My interest is in cosmology and I was seeking a simple UNCOMPLICATED answer about emission from these masses and the gravitational potential within which the occur. The conclusions regarding galactic rotation curves etc made from observations still don't make sense to me, but I have decided to back off from trying to extract a "rule of thumb" regarding how GR affects our observations. As you say, we seem to be going in circles. I thank you for your patience. Regards. Pierre.

Dale
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Hi DaleSpam. Thanks for your attempts to help me. My interest is in cosmology and I was seeking a simple UNCOMPLICATED answer about emission from these masses and the gravitational potential within which the occur. The conclusions regarding galactic rotation curves etc made from observations still don't make sense to me, but I have decided to back off from trying to extract a "rule of thumb" regarding how GR affects our observations. As you say, we seem to be going in circles. I thank you for your patience. Regards. Pierre.
You are quite welcome. For an uncomplicated answer I would just stick with post #35, everything else is just window-dressing and confusion.